Mathematics › Application of Derivative
Application of Derivative Questions
300 questions across 9 subtopics — with step-by-step solutions.
Error approximation(8)
- The shortest distance between the curves a... | Mathematics | TestHub
- A spherical chocolate ball has a layer of... | Mathematics | TestHub
- If the function , where , attains its loca... | Mathematics | TestHub
- Let be a function defined by . If is the n... | Mathematics | TestHub
- Let . If the function attains its local ma... | Mathematics | TestHub
- Let and be the critical points of the func... | Mathematics | TestHub
- The sum of all local minimum values of the... | Mathematics | TestHub
- Let f be a differentiable function on such... | Mathematics | TestHub
Maxima-Minima(179)
- The maximum distance from origin of a poin... | Mathematics | TestHub
- If the function , where , attains its maxi... | Mathematics | TestHub
- The real number when added to its inverse... | Mathematics | TestHub
- A function has a second order derivative .... | Mathematics | TestHub
- If , then at least one root of the equatio... | Mathematics | TestHub
- A point on the parabola at which the ordin... | Mathematics | TestHub
- If is a real-valued differentiable functio... | Mathematics | TestHub
- If the equation , has a positive root , th... | Mathematics | TestHub
- Area of the greatest rectangle that can be... | Mathematics | TestHub
- A spherical iron ball in radius is coated... | Mathematics | TestHub
- Practice Question | Mathematics | TestHub
- If is cubic polynomial which has local max... | Mathematics | TestHub
- If is real, the maximum value of is | Mathematics | TestHub
- The function has a local minimum at | Mathematics | TestHub
- Paragraph:Read the following passage and a... | Mathematics | TestHub
- Suppose the cube has three distinct real r... | Mathematics | TestHub
- How many real solutions does the equation... | Mathematics | TestHub
- The total number of local maxima and local... | Mathematics | TestHub
- Let be a polynomial of degree 4 having ext... | Mathematics | TestHub
- The shortest distance between the line and... | Mathematics | TestHub
- Given such that is the only real root of .... | Mathematics | TestHub
- For the function , | Mathematics | TestHub
- The maximum value of the function on the s... | Mathematics | TestHub
- Paragraph:Consider the polynomial . Let be... | Mathematics | TestHub
- Let be a function defined on (the set of a... | Mathematics | TestHub
- Let and be real-valued functions defined o... | Mathematics | TestHub
- Paragraph:Consider the polynomial . Let be... | Mathematics | TestHub
- Let be defined by . If has a local minimum... | Mathematics | TestHub
- The maximum value of the expression is | Mathematics | TestHub
- The shortest distance between line and cur... | Mathematics | TestHub
- If a circular iron sheet of radius is heat... | Mathematics | TestHub
- Let be a real polynomial of least degree w... | Mathematics | TestHub
- If for all , then | Mathematics | TestHub
- Let be such that the function given by has... | Mathematics | TestHub
- The weight of a certain stock of fish is g... | Mathematics | TestHub
- If a metallic circular plate of radius is... | Mathematics | TestHub
- Let be defined by Statement 1: The functio... | Mathematics | TestHub
- Consider a rectangle whose length is incre... | Mathematics | TestHub
- A spherical balloon is filled with cubic m... | Mathematics | TestHub
- Let be defined as . The total number of po... | Mathematics | TestHub
- Let for all and let for all . Question:Whi... | Mathematics | TestHub
- A spherical balloon is being inflated at t... | Mathematics | TestHub
- The maximum area of a right angled triangl... | Mathematics | TestHub
- The functionhas a local minimum or a local... | Mathematics | TestHub
- Let and for . The possible value of lies i... | Mathematics | TestHub
- If the surface area of a sphere of radius... | Mathematics | TestHub
- A line L :meetsat E(0,3) and the arc of th... | Mathematics | TestHub
- The cost of running a bus from point to po... | Mathematics | TestHub
- A rectangular sheet of fixed perimeter wit... | Mathematics | TestHub
- The volume of the largest possible right c... | Mathematics | TestHub
- If non-zero real numbersandare such that,... | Mathematics | TestHub
- Ifthen the equationhas : | Mathematics | TestHub
- If the volume of a spherical ball is incre... | Mathematics | TestHub
- Ifandare extreme points of, then | Mathematics | TestHub
- Let be a polynomial of degree four and hav... | Mathematics | TestHub
- A cylindrical container is to be made from... | Mathematics | TestHub
- Letandbe the minimum and the maximum value... | Mathematics | TestHub
- LetThen,is an increasing function in the i... | Mathematics | TestHub
- The minimum distance of a point on the cur... | Mathematics | TestHub
- The least value offor which,for allis | Mathematics | TestHub
- A wire of lengthunits is cut into two part... | Mathematics | TestHub
- Twenty meters of wire is available for fen... | Mathematics | TestHub
- Ifthen | Mathematics | TestHub
- If a right circular cone, having maximum v... | Mathematics | TestHub
- LetandIf, then the local minimum value ofis: | Mathematics | TestHub
- Letandbe respectively the absolute maximum... | Mathematics | TestHub
- If a right circularcone having maximum vol... | Mathematics | TestHub
- If is a quadratic expression such that (2)... | Mathematics | TestHub
- Let be a polynomial of degree 4 having ext... | Mathematics | TestHub
- Letand. Then the set of all, where the fun... | Mathematics | TestHub
- LetandIfattains maximum value atandattains... | Mathematics | TestHub
- Let be positive real numbers and positive... | Mathematics | TestHub
- Letbe given byThen which of the following... | Mathematics | TestHub
- The maximum volumeof the right circular co... | Mathematics | TestHub
- Letbe given byDefineThen which of the foll... | Mathematics | TestHub
- LetLetbe all the points of local maximum o... | Mathematics | TestHub
- Ifis a non-zero polynomial of degree four,... | Mathematics | TestHub
- Ifis the minimum value offor which the fun... | Mathematics | TestHub
- Themaximum value of the finction on the se... | Mathematics | TestHub
- Letbe a twice differentiable function such... | Mathematics | TestHub
- Ifandare respectively the sets of local mi... | Mathematics | TestHub
- The height of a right circular cylinder of... | Mathematics | TestHub
- The maximum area (in sq. units) of a recta... | Mathematics | TestHub
- Let the function be defined by . Suppose t... | Mathematics | TestHub
- Let a function be continuous, and be defin... | Mathematics | TestHub
- Letandbe two vertical poles atrespectively... | Mathematics | TestHub
- Letbe a polynomial of degreesuch thatare i... | Mathematics | TestHub
- Ifbe a polynomial of degree three that has... | Mathematics | TestHub
- Let, be a polynomial of degree, such that,... | Mathematics | TestHub
- The set of all real valuesfor which the fu... | Mathematics | TestHub
- The area (in sq. units) of the largest rec... | Mathematics | TestHub
- Consider all rectangles lying in the regio... | Mathematics | TestHub
- Letbe amatrix, whereLet a functionbe defin... | Mathematics | TestHub
- A wire of length is to be cut into two pie... | Mathematics | TestHub
- Let and be defined by and where, for any p... | Mathematics | TestHub
- Letbe a cubic polynomial withand has a loc... | Mathematics | TestHub
- Letbe defined asfor allwheresuch thatand f... | Mathematics | TestHub
- Let and be defined by f_{2}(x)=98(x-1)^{50... | Mathematics | TestHub
- Letandrespectively be the maximum and mini... | Mathematics | TestHub
- Letbe a polynomial of degreeinin which the... | Mathematics | TestHub
- A wire of lengthis cut into two pieces, on... | Mathematics | TestHub
- The maximum slope of the curve occurs at t... | Mathematics | TestHub
- If a rectangle is inscribed in an equilate... | Mathematics | TestHub
- The triangle of maximum area that can be i... | Mathematics | TestHub
- Letbe a real number such that the function... | Mathematics | TestHub
- The local maximum value of the function,is | Mathematics | TestHub
- The sum of all the local minimum values of... | Mathematics | TestHub
- Letbe a real polynomial of degreewhich van... | Mathematics | TestHub
- Let be defined by Then which of the follow... | Mathematics | TestHub
- A box open from top is made from a rectang... | Mathematics | TestHub
- Ifandrespectively are the number of local... | Mathematics | TestHub
- Letandbe any points on the curvesand, resp... | Mathematics | TestHub
- The sum of the absolute minimum and the ab... | Mathematics | TestHub
- The sum of the absolute maximum and absolu... | Mathematics | TestHub
- Let . Then which of the following statemen... | Mathematics | TestHub
- The sum of absolute maximum and absolute m... | Mathematics | TestHub
- If the absolute maximum value of the funct... | Mathematics | TestHub
- LetThen the set of all values of, for whic... | Mathematics | TestHub
- The lengths of the sides of a triangle are... | Mathematics | TestHub
- Letbe a function defined by. The, which of... | Mathematics | TestHub
- A wire of lengthis to be cut into two piec... | Mathematics | TestHub
- The curvetouches the-axis at the pointand... | Mathematics | TestHub
- Letbe a twice differentiable function insu... | Mathematics | TestHub
- Let. Ifandare respectively the number of p... | Mathematics | TestHub
- Consider a cuboid of sidesandand a closed... | Mathematics | TestHub
- A wire of lengthis to be cut into two piec... | Mathematics | TestHub
- Ifis the greatest term in the sequencethen... | Mathematics | TestHub
- Practice Question | Mathematics | TestHub
- The absolute minimum value, of the functio... | Mathematics | TestHub
- Let. Ifandrespectively are the maximum and... | Mathematics | TestHub
- In the figure, and . If the area of is , w... | Mathematics | TestHub
- Letbe a local minima of the function. Ifis... | Mathematics | TestHub
- The sum of the abosolute maximum and minim... | Mathematics | TestHub
- Let the functionhave a maxima for some val... | Mathematics | TestHub
- If the total maximum value of the function... | Mathematics | TestHub
- Let the set of all positive values of , fo... | Mathematics | TestHub
- Let be a real valued function. If and are... | Mathematics | TestHub
- A variable line passes through the point a... | Mathematics | TestHub
- Let . The number of points of local maxima... | Mathematics | TestHub
- Let a rectangle of sides 2 and 4 be inscri... | Mathematics | TestHub
- Let the maximum and minimum values of be a... | Mathematics | TestHub
- The function, has | Mathematics | TestHub
- Let. Ifandare the maximum and minimum valu... | Mathematics | TestHub
- If the function attains the maximum value... | Mathematics | TestHub
- If the function has a local maximum at and... | Mathematics | TestHub
- Let be the region enclosed by the parabola... | Mathematics | TestHub
- Let denote the set of all real numbers. Fo... | Mathematics | TestHub
- Let f be a differentiable function on such... | Mathematics | TestHub
- Let be a polynomial function of degree fou... | Mathematics | TestHub
- The sum of all local minimum values of the... | Mathematics | TestHub
- Let . If the function attains its local ma... | Mathematics | TestHub
- If the set of all values of a, for which t... | Mathematics | TestHub
- Let and be the critical points of the func... | Mathematics | TestHub
- If the function , where , attains its loca... | Mathematics | TestHub
- If and if has a local maxima at , then, th... | Mathematics | TestHub
- Point on the curve which is nearest to the... | Mathematics | TestHub
- From a point perpendicular tangents are dr... | Mathematics | TestHub
- If the equation x^{3}-9 x^{2}+24 x+k=0 has... | Mathematics | TestHub
- The maximum value of the function f(x)=2 x... | Mathematics | TestHub
- Minimum value of \frac{(6+x)(11+x)}{2+x} is | Mathematics | TestHub
- The Value of 'a' for which has an extremum... | Mathematics | TestHub
- The maximum value of x^{-x},(x>0) is | Mathematics | TestHub
- The maximum area of a rectangle inscribed... | Mathematics | TestHub
- Practice Question | Mathematics | TestHub
- Let f(x)=\frac{e^{x}}{1+x^{2}} and g(x)=f^... | Mathematics | TestHub
- The diagonal of the rectangle of maximum a... | Mathematics | TestHub
- Let \mathrm{f}(\mathrm{x})=\mathrm{x}^{2}-... | Mathematics | TestHub
- A rectangle is inscribed in an equilateral... | Mathematics | TestHub
- The interval in which the function , is st... | Mathematics | TestHub
- In (0,2 \pi), f(x)=x+\sin 2 x is | Mathematics | TestHub
- If and if has a local maxima at , then, gr... | Mathematics | TestHub
- Let \mathrm{f}(\mathrm{x}) be a positive d... | Mathematics | TestHub
- The minimum value of f(x)=x^{2}+\frac{250}... | Mathematics | TestHub
- For the function consider the following tw... | Mathematics | TestHub
- If the function \mathrm{f}(\mathrm{x})=\le... | Mathematics | TestHub
- Match List-I with List-II and select the c... | Mathematics | TestHub
- The least value of 'a' for which the equat... | Mathematics | TestHub
- The greatest value of \mathrm{f}(\mathrm{x... | Mathematics | TestHub
- The largest area of the rectangle which ha... | Mathematics | TestHub
Maxima-Minima- Word problems(8)
- Which fraction exceeds its p^{\text {th }}... | Mathematics | TestHub
- A window is in the shape of a rectangle su... | Mathematics | TestHub
- A sector subtends an angle 2 \alpha at the... | Mathematics | TestHub
- The maximum area of a rectangle whose two... | Mathematics | TestHub
- A person wishes to lay a straight fence ac... | Mathematics | TestHub
- A point ' P ' is given on the circumferenc... | Mathematics | TestHub
- Two runners A and B start at the origin an... | Mathematics | TestHub
- The sum of two numbers is ' 6 '. The minim... | Mathematics | TestHub
Miscellaneous/Mixed(2)
Monotonicity-Increasing-Decreasing(79)
- A function is matched below against an int... | Mathematics | TestHub
- Let . | Mathematics | TestHub
- The function is an increasing function in | Mathematics | TestHub
- Let be a non-constant twice differentiable... | Mathematics | TestHub
- Let the function be given by . Then, is | Mathematics | TestHub
- Paragraph:Consider the function defined by... | Mathematics | TestHub
- Paragraph:Consider the function defined by... | Mathematics | TestHub
- The number of distinct real roots of is | Mathematics | TestHub
- If , then is | Mathematics | TestHub
- Statement-1: The function is increasing fo... | Mathematics | TestHub
- Statement-1: The equation is satisfied by... | Mathematics | TestHub
- Letbe given bythen | Mathematics | TestHub
- Letbe continuous functions which are twice... | Mathematics | TestHub
- Paragraph: Let be a thrice differentiable... | Mathematics | TestHub
- The total number of distinctfor which,is | Mathematics | TestHub
- Let, be a continuous function then, which... | Mathematics | TestHub
- LetColumn 1 contains information about zer... | Mathematics | TestHub
- LetColumn 1 contains information about zer... | Mathematics | TestHub
- The functiondefined byis: | Mathematics | TestHub
- LetColumn 1 contains information about zer... | Mathematics | TestHub
- The number of real solutions of the equati... | Mathematics | TestHub
- Let wherea, b and d are non-zero real cons... | Mathematics | TestHub
- If the functiongiven by, for someis increa... | Mathematics | TestHub
- Ifis a critical point of the functionthen | Mathematics | TestHub
- Letbe defined byand. Then the function | Mathematics | TestHub
- Supposeis a polynomial of degree four havi... | Mathematics | TestHub
- Letthen which of the following is true? | Mathematics | TestHub
- The function,, is increasing for alllying in | Mathematics | TestHub
- Consider the functiondefined byThenis: | Mathematics | TestHub
- Let,. Then,is : | Mathematics | TestHub
- The number of distinct real roots of the e... | Mathematics | TestHub
- The minimum value offor which the equation... | Mathematics | TestHub
- Ifis the least value ofsuch that the funct... | Mathematics | TestHub
- Letbe an integer such that all the real ro... | Mathematics | TestHub
- The function: | Mathematics | TestHub
- Let be a real valued function, defined on... | Mathematics | TestHub
- The number of real roots of the equationis: | Mathematics | TestHub
- Let be defined as Then is increasing funct... | Mathematics | TestHub
- Paragraph: Let and be functions such that... | Mathematics | TestHub
- The function is such that . Consider two s... | Mathematics | TestHub
- Let be defined asLet is increasing}. Then... | Mathematics | TestHub
- Paragraph: Let and be functions such that... | Mathematics | TestHub
- The range offor which the function, has cr... | Mathematics | TestHub
- Letandbe two functions defined byandThen,... | Mathematics | TestHub
- The number of distinct real roots of the e... | Mathematics | TestHub
- Letbe the largest value offor which the fu... | Mathematics | TestHub
- Let the function, be decreasing inand incr... | Mathematics | TestHub
- Let. Ifis the range of the function, theni... | Mathematics | TestHub
- The function, is | Mathematics | TestHub
- If the maximum value of, for which the fun... | Mathematics | TestHub
- For the function, which one of the followi... | Mathematics | TestHub
- The number of distinct real roots ofis | Mathematics | TestHub
- The number of real solutions ofis equal to... | Mathematics | TestHub
- The number of distinct real roots of the e... | Mathematics | TestHub
- If the sum of all the roots of the equatio... | Mathematics | TestHub
- If the functionsandhave a common extreme p... | Mathematics | TestHub
- Letand. Then | Mathematics | TestHub
- Let be a differentiable function such that... | Mathematics | TestHub
- The set of all for which the equation has... | Mathematics | TestHub
- Letand. Ifis decreasing in the intervaland... | Mathematics | TestHub
- Ifand, then the value ofis equal to _____ . | Mathematics | TestHub
- Let S be the set of all twice differentiab... | Mathematics | TestHub
- The number of points, where the curve cros... | Mathematics | TestHub
- For the function , between the following t... | Mathematics | TestHub
- The number of critical points of the funct... | Mathematics | TestHub
- The function | Mathematics | TestHub
- Let the set of all values of , for which d... | Mathematics | TestHub
- Ifandthenis strictly increasing in: | Mathematics | TestHub
- Let the function be defined by . Then the... | Mathematics | TestHub
- Letandfor all. Ifis decreasing inand incre... | Mathematics | TestHub
- Let the function be strictly increasing in... | Mathematics | TestHub
- Let denote the set of all real numbers. Le... | Mathematics | TestHub
- Let denote the set of all real numbers. De... | Mathematics | TestHub
- Let be a function defined by . If is the n... | Mathematics | TestHub
- Let be the largest open interval in which... | Mathematics | TestHub
- Consider f(\mathrm{x})=\frac{\ell \mathrm{... | Mathematics | TestHub
- Let \beta \in \mathbb{R} and let \mathrm{f... | Mathematics | TestHub
- Let domain and range of f(x) and g(x) are... | Mathematics | TestHub
- Let f and g be two real valued differentia... | Mathematics | TestHub
Monotonicity-LMVT(2)
Monotonicity-Rolle's-theroem(3)
Rate Measure(12)
- If is so small that and higher powers of m... | Mathematics | TestHub
- A spherical iron ball of radiusis coated w... | Mathematics | TestHub
- A water tank has the shape of an inverted... | Mathematics | TestHub
- Am ladder leans against a vertical wall. I... | Mathematics | TestHub
- The position of a moving car at timeis giv... | Mathematics | TestHub
- A spherical iron ball ofradius is coated w... | Mathematics | TestHub
- If the surface area of a cube is increasin... | Mathematics | TestHub
- A water tank has the shape of a right circ... | Mathematics | TestHub
- Water is being filled at the rate ofin a r... | Mathematics | TestHub
- A square piece of tin of sideis to be made... | Mathematics | TestHub
- A spherical chocolate ball has a layer of... | Mathematics | TestHub
- If the petrol burnt per hour in driving a... | Mathematics | TestHub
Tangents & Normals(7)
- Tangent is drawn at any point of a curve w... | Mathematics | TestHub
- The tangent to the curve drawn at the poin... | Mathematics | TestHub
- The slope of the tangent to the curveat th... | Mathematics | TestHub
- Letandbe positive real numbers. Supposeis... | Mathematics | TestHub
- The shortest distance between the curves a... | Mathematics | TestHub
- Consider the curve y=e^{2 x^{2}}+2 x , the... | Mathematics | TestHub
- If \mathrm{y}=\mathrm{x}^{3}-\mathrm{c} an... | Mathematics | TestHub
Practice Application of Derivative on TestHub
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