JEE Main 2021MathematicsApplication of DerivativesMediumNumerical

JEE Main 2021 — Application of Derivatives Question with Solution

JEE Main 2021 (31 Aug Shift 2)

Question

Let fx be a cubic polynomial with f1=-10, f-1=6, and has a local minima at x=1, and f'x has a local minima at x=-1. Then f3 is equal to                .

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Show full solutionCorrect answer: 22
Correct answer
22

Step-by-step explanation

Let, fx=ax3+bx2+cx+d

Diff w. r. t.  'x'

f'x=3ax2+2bx+c

Again diff. w. r. t.  'x'

f"x=6ax+2b

f"-1=0

-6a+2b=0

b=3a

f'1=0

3a+6a+c=0

c=-9a

f1=-10 

-5a+d=-10      …i

f(-1)=6 

11a+d=6       …ii

From equations i-ii

We get a=1, d=-5, b=3, c=-9

Then, fx=x3+3x2-9x-5

Hence,  f3=27+27-27-5

f3=22

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About this question

This is a previous-year question from JEE Main 2021, covering the Application of Derivatives chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.