Wholesum differentiability

Calculus Level 3

Consider the following function f ( x ) = ( α + x ) 2 e ( 5 x ) 2 f(x)=(\alpha+|x|)^{2}e^{(5-|x|)^{2}} Find the sum of all the values of α \alpha for which f ( x ) f(x) is differentiable for all x R x\in\mathbb{R} .


The answer is 0.2.

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