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

Answer:

$f'(0)=0$

Step-by-step explanation:

Applying the chain rule

$\frac{d}{dx} (f(-x))=-\frac{df}{dx}$

Then it becomes

$\frac{df}{dx} =-\frac{df}{dx}$

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

$f'(0)=0$