JEE Main 2025 — Continuity and Differentiability Question with Solution
JEE Main 2025 (22 Jan Shift 1)
Question
Let the function,
be differentiable for all , where . If the area of the region enclosed by and the line is , then the value of is ________
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Show full solutionCorrect answer: 34
Correct answer
34
Step-by-step explanation
is continuous and differentiable
$\begin{aligned}
& \text { at } x=1, \mathrm{LHL}=\mathrm{RHL}, \mathrm{LHD}=\mathrm{RHD} \\
& -3 a-2=a^2+b,-6 a=b \\
& a=2 ; b=-12 \\
& f(x)=\left\{\begin{array}{cc}
-6 x^2-2, & x < 1 \\
4-12 x, & x \geq 1
\end{array}\right.
\end{aligned}$
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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.