JEE Main 2025 — Continuity and Differentiability Question with Solution
JEE Main 2025 (22 Jan Shift 1)
Question
Let be a real differentiable function such that and for all . Then is equal to :
Choose an option
Show full solutionCorrect option: A
Correct answer
A
Step-by-step explanation
....(i)
And ....(ii)
Now replace by zero and by zero we get
$\begin{aligned}
& f(0)=f(0) f(0)+f(0) f(0) \\
& 1=f(0)+f(0) \\
& \therefore \quad f^{\prime}(0)=\frac{1}{2} ...(iii)
\end{aligned}$
Now replace by zero in equation (i), we get
or,
then
hence
Put , we get
Then
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This is a previous-year question from JEE Main 2025, 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.