JEE Main 2023MathematicsApplication Of DerivativesMean Value TheoremhardMCQ

JEE Main 2023Application Of Derivatives Question with Solution

From: JEE Main 2023 (Online) 11th April Morning Shift

Question

Let be a differentiable function such that with and .

Consider the following two statements :

(A) : , for all

(B) : , for all

Then,

Choose an option

Show full solutionCorrect option: D
Correct answer
DBoth the statements and (B) are true

Step-by-step explanation

Given,







Let

As $g(x) \geq 0, \forall x \in[2,4], g(x)[2,4]$





As, is an increasing function,











Now,





Hence, both statements and are true.

Note : LMVT on not satisfied.

Hence no such function exists.

Therefore it should be bonus.

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About this question

This is a previous-year question from JEE Main 2023, 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.