JEE Main 2020MathematicsApplication of DerivativesMediumMCQ

JEE Main 2020 — Application of Derivatives Question with Solution

JEE Main 2020 (05 Sep Shift 2)

Question

If x=1 is a critical point of the function f(x)=3x2+ax-2-aex, then 

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Show full solutionCorrect option: D
Correct answer
Dx=1 is a local minima andx=-23 are local maxima of f

Step-by-step explanation

f(x)=3x2+ax-2-aex
f'(x)=3x2+ax-2-aex+ex(6x+a)=ex3x2+(a+6)x-2

∵  x=1 is a critical point   ∴  f'(1)=0

∴3+a+6-2=0
a=-7

∴f'(x)=ex3x2-x-2=ex3x2-3x+2x-2=ex(3x+2)(x-1)

∴ maxima at x=-2 3∴ minima at x=1

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About this question

This is a previous-year question from JEE Main 2020, 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.