JEE Main 2024MathematicsDifferentiationMediumNumerical

JEE Main 2024 — Differentiation Question with Solution

JEE Main 2024 (27 Jan Shift 1)

Question

Let for a differentiable function f:(0,∞)→R, fx-fy≥logexy+x-y,∀x,y∈0,∞. Then ∑n=120f'1n2 is equal to

Enter your answer

Show full solutionCorrect answer: 2890
Correct answer
2890

Step-by-step explanation

Given: fx-fy≥logexy+x-y

Now, taking x=x+h & y=x we get,

fx+h-fx≥logex+hx+x+h-x

fx+h-fx≥logex+hx+h

Now, using f'x=limh→0fx+h-fxh

⇒f'x=limh→0logex+hx+hh

⇒f'x=limh→0loge1+hxx·hx+1

⇒f'x=1x+1

⇒f'1x2=x2+1

⇒∑x=120f'1x2=∑x=120x2+1

⇒∑x=120f'1x2=∑x=120x2+20

⇒∑x=120f'1x2=20×21×416+20

⇒∑x=120f'1x2=2870+20

⇒∑x=120f'1x2=2890

Practice this on the real CBT interface

Solve this JEE Main question (and the rest of the Differentiation chapter) on PrepSharp's TCS iON-style CBT player — with timer, bookmarks and session analytics.

Solve interactively →

About this question

This is a previous-year question from JEE Main 2024, covering the Differentiation 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.