# Help w/ Differentiability

• February 13th 2010, 11:59 PM
Endowed
Help w/ Differentiability
we have $f,g : [a,b] \to \mathbb{R}$. If the statement is false provide counterexample and if true prove it. If $f = g^2$ and $f$ is differentiable on $[a,b]$, then $g$ is differentiable on $(a,b)$.

• February 14th 2010, 01:42 AM
Jhevon
Quote:

Originally Posted by Endowed
we have $f,g : [a,b] \to \mathbb{R}$. If the statement is false provide counterexample and if true prove it. If $f = g^2$ and $f$ is differentiable on $[a,b]$, then $g$ is differentiable on $(a,b)$.

(I interpret $g^2$ to mean $g(x) \cdot g(x)$ as opposed to something like $(g \circ g)(x)$)
Take $g(x) = \left \{ \begin{matrix} 1 & \text{ if } x \ge 0 \\ -1 & \text{ if } x < 0 \end{matrix} \right.$