Help w/ Differentiability

**Endowed** · February 13th 2010, 10:59 PM

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 $(a,b)$ .

Please help a brother get started.

**Jhevon** · February 14th 2010, 12:42 AM

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 $(a,b)$ .

Please help a brother get started.

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

False.

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

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

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