Question

Suppose \(g:\mathbb R\rightarrow \mathbb R\) is an everywhere differentiable function. Show that if \(g(a)\neq 0\), then \(|g(x)|\) is differentiable at x =a.
Hint: use the fact that composition of 2 differentiable functions is differentiable.
b) Now suppose g(a) =0. Show that \(|g(x)| \) is differentiable at x = a iff g'(a) =0
Please, help

Answer 1

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