Mathematics - Application of Derivative Question with Solution | TestHub

MathematicsApplication of DerivativeTangents & NormalsEasy2 minQB

MathematicsEasyinteger

The curve $y = a x^{3} + b x^{2} + c x + 5$ , touches the $x$ -axis at $P (- 2, 0)$ and cuts the $y$ -axis at a point $Q$ , where its gradient is 3 , then find the value of $4 b - 2 a + c$ .

Answer:

Solution:

Let $y = f (x), f^{'} (- 2) = 0, f (- 2) = 0$

$f^{'} (0) = 3, f^{'} (x) = 3 ax^{2} + 2 bx + c$

Solving $a = - \frac{1}{2}, b = - \frac{3}{4}$ and $c = 3$

$\Rightarrow 4 b - 2 a + c = 1$

Stream:JEESubject:MathematicsTopic:Application of DerivativeSubtopic:Tangents & Normals

⏱ 2mℹ️ Source: QB

Doubts & Discussion

Loading discussions...