JEE Main 2014 — Continuity and Differentiability Question with Solution
JEE Main 2014 (11 Apr Online)
Question
Let and . Then
Choose an option
Show full solutionCorrect option: C
Correct answer
C is continuous at but it is not differentiable at
Step-by-step explanation
Let and
Since, L.H.L and R.H.L at of is equal to 0 therefore is continuous at
Now, suppose is differentiable
Since, L.H.L and R.H.L at of are different therefore is not continuous.
is not differentiable
our assumption is wrong
Hence is not differentiable at .
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 2014, 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.