(All Steps) Suppose that f:R→ R is differentiable at c and that f(c)=0. Show that g(x)=|f(x)| is differentiable at c if and only if
Question: Suppose that \(f:R\to R\) is differentiable at c and that \(f\left( c \right)=0\). Show that \(g\left( x \right)=|f\left( x \right)|\) is differentiable at c if and only if \(f'\left( c \right)=0\)
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![[Step-by-Step] If f:R→ R is differentiable at](/images/solutions/MC-solution-library-31055.jpg "[Step-by-Step] If f:R→ R is differentiable at c , prove that")
[Step-by-Step] If f:R→ R is differentiable at c , prove that
(All Steps) Given that the function h(x)=x^3+2x+1 for x ∈ R has
![[Solution Library] Use the Mean Value Theorem](/images/solutions/MC-solution-library-31057.jpg "[Solution Library] Use the Mean Value Theorem to prove that (x-1)/(x)≤")
[Solution Library] Use the Mean Value Theorem to prove that (x-1)/(x)≤
![[Solution Library] Let I be an interval](/images/solutions/MC-solution-library-31058.jpg "[Solution Library] Let I be an interval and let f:I→ R be differentiable")
[Solution Library] Let I be an interval and let f:I→ R be differentiable
(Step-by-Step) Let f(x) = x^2 for x rational, let f(x) = 0 for x
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