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Math Help - Help w/ Differentiability

  1. #1
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    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).

    Please help a brother get started.
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Endowed View Post
    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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