JEE Main 2019MathematicsContinuity and DifferentiabilityEasyMCQ

JEE Main 2019 — Continuity and Differentiability Question with Solution

JEE Main 2019 (10 Apr Shift 1)

Question

Let f:R→R be differentiable at c∈R and fc=0. If gx=fx, then at x=c, g is:

Choose an option

Show full solutionCorrect option: C
Correct answer
Cdifferentiable if f'c=0

Step-by-step explanation

Given gx=fx and fc=0

g'c+=limx→c+fx-fcx-c=limx→c+fx-f(c)x-c, as x>c

⇒g'c+=f'c

gc-=limx→c-fx-fcx-c=-limx→c-fx-f(c)x-c, as x<c

⇒g'c-=-f'c

For gx to be differentiable at x=c, f'c must be 0. Else, it is non-differentiable.

Practice this on the real CBT interface

Solve this JEE Main question (and the rest of the Continuity and Differentiability 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 2019, covering the Continuity and Differentiability 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.