Mathematics - Application of Derivative Question with Solution | TestHub

MathematicsApplication of DerivativeMaxima-MinimaMedium2 minPYQ_2021
MathematicsMediumnumerical

LetP(x)be a real polynomial of degree3which vanishes atx=-3. LetP(x)have local minima atx=1, local maxima atx=-1and∫-11Pxdx=18, then the sum of all the coefficients of the polynomialP(x)is equal to ___ .

Answer:
8.00
Solution:

Let P'(x)=a(x-1)(x+1)=ax2-1

Px=a∫x2-1dx+c

=ax33-x+c

Now P(-3)=0

⇒a-273+3+c=0

⇒-6a+c=0  …(1)

Now ∫-11ax33-x+cdx=18

=2c=18⇒c=9  ...2

 From (1) & (2) ⇒-6a+9=0⇒a=32

⇒Px=32x33-x+9

Then, the Sum of coefficient=12-32+9

=8

Stream:JEESubject:MathematicsTopic:Application of DerivativeSubtopic:Maxima-Minima
⏱ 2mℹ️ Source: PYQ_2021

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