# Help w/ Differentiability

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• Feb 13th 2010, 10:59 PM
Endowed
Help w/ Differentiability
we have $\displaystyle f,g : [a,b] \to \mathbb{R}$. If the statement is false provide counterexample and if true prove it. If $\displaystyle f = g^2$ and $\displaystyle f$ is differentiable on $\displaystyle [a,b]$, then $\displaystyle g$ is differentiable on $\displaystyle (a,b)$.

Please help a brother get started. (Nod)
• Feb 14th 2010, 12:42 AM
Jhevon
Quote:

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

Please help a brother get started. (Nod)

(I interpret $\displaystyle g^2$ to mean $\displaystyle g(x) \cdot g(x)$ as opposed to something like $\displaystyle (g \circ g)(x)$)

False.

Take $\displaystyle g(x) = \left \{ \begin{matrix} 1 & \text{ if } x \ge 0 \\ -1 & \text{ if } x < 0 \end{matrix} \right.$

and take [a,b] to be any closed interval containing the origin.