JEE MATHEMATICS MCQ: DIFFERENTIATION

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Application +4 | -1

f(x)=\left\{\begin{array}{ll}e^x, & x<2 \\ a x+b, & x \geq 2\end{array}\right.

is differentiable for all

x \in R

, then

View answer and explanation

Correct option: A

a=e^2, b=-e^2

Option A is correct because for the function to be differentiable at

x=2

, both continuity and differentiability must hold, leading to

a=e^2

and

b=-e^2

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