Let \( f(x) \) be a differentiable and \( \mathrm{g}(\mathrm{x}) \) be a twice differentiable fu...

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Let \( f(x) \) be a differentiable and \( \mathrm{g}(\mathrm{x}) \) be a twice differentiable function such that \( |f(x)-1| \leq 1 \) and \( f^{\prime}(x)=g(x) \). If \( f^{2}(3)+g^{2}(3) \) \( =20 \) then number of values of \( c \in(0,4) \) such that \( g(c) g^{\prime \prime}(c) \) 0 is/are
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