JEE Main 2022MathematicsApplication of DerivativesEasyMCQ

JEE Main 2022 — Application of Derivatives Question with Solution

JEE Main 2022 (28 Jul Shift 2)

Question

The function fx=xex1-x,x∈R, is

Choose an option

Show full solutionCorrect option: A
Correct answer
Aincreasing in -12,1

Step-by-step explanation

Let fx=xex1-x then fx is:

Now fx=xex1-x

Differentiating both side w.r.t x we get,

f'x=xex1-x1-2x+ex1-x

=-ex1-x2x2-x-1

=-ex1-x2x+1x-1

Now finding critical point by equating f'x=0

We get, x=-12 & x=1

∴  fx is decreasing in -∞,-12∪1,∞

And increasing in -12,1

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About this question

This is a previous-year question from JEE Main 2022, 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.