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Let f be a differentiable function on (-0o,00) such that f(-x)= f(x) for all x in (, o). Compute the value of f'(0). Justify your answer

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Answer:


f'(0)=0

Explanation:

Applying the chain rule


(d)/(dx) (f(-x))=-(df)/(dx)

Then it becomes


(df)/(dx) =-(df)/(dx)

In x=0


\frac{d[tex]f'(0)=-f'(0)\\f'(0)+f'(0)=0\\2f'(0)=0\\f}{dx} =-\frac{df}{dx}[/tex]

Then


f'(0)=0

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