Question

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

Answer 1

`f'(0)=0`

Explanation:

Applying the chain rule

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

Then it becomes

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

In x=0

f}{dx} =-\frac{df}{dx}[/tex]

Then

`f'(0)=0`