Answer:
[tex]f'(0)=0[/tex]
Step-by-step explanation:
Applying the chain rule
[tex]\frac{d}{dx} (f(-x))=-\frac{df}{dx}[/tex]
Then it becomes
[tex]\frac{df}{dx} =-\frac{df}{dx}[/tex]
In x=0
[tex]\frac{d[tex]f'(0)=-f'(0)\\f'(0)+f'(0)=0\\2f'(0)=0\\[/tex]f}{dx} =-\frac{df}{dx}[/tex]
Then
[tex]f'(0)=0[/tex]
