JEE Main 2022MathematicsApplication of DerivativesMediumMCQ

JEE Main 2022 — Application of Derivatives Question with Solution

JEE Main 2022 (27 Jun Shift 2)

Question

If m and n respectively are the number of local maximum and local minimum points of the function fx=∫0x2t2-5t+42+etdt, then the ordered pair m,n is equal to

Choose an option

Show full solutionCorrect option: A
Correct answer
A2,3

Step-by-step explanation

Given fx=∫0x2t2-5t+42+etdt

We know that,

ddx∫uxvxfvdx=fvxddxvu-fuxddxux

Using above formula we get f'x=x4-5x2+42+ex2·2x

For critical points f'x=0

So, xx2-1x2-42+ex2=0

⇒xx+1x-1x+2x-2=0

Now by first derivative test we get,

Here points of maxima are -1,1  & points of minima are -2,0,2

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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.