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  4. The function f(x) = a sin|x| + be|x| is differentiable at x = 0 when

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Q. The function $f(x) = a \sin|x| + be^{|x|}$ is differentiable at $x = 0$ when

WBJEEWBJEE 2014Continuity and Differentiability

Solution:

Given, $f(x)=a \sin |x|+b e^{|x|}$
We know that $\sin |x|$ and $e^{|x|}$ is not differentiable at $x=0$
Therefore, for $f(x)$ to differentiable at $x=0$,
we must have $a=b=0$
$\therefore a+b=0$