Respuesta :
The derivative of an odd function is even, and even functions satisfy f(-x)=f(x).
If g is an odd function and g'(3) = 4, g'(−3) = 4.
What is derivative of odd functions?
The derivative of odd function is always an even function i.e., f'(-x) = f'(x).
We know that f(-x) = -f(x)
Taking derivative on both sides.
[tex]\frac{d}{dx}(f(-x)) = \frac{d}{dx} (- f(x))\\\\f'(-x)\frac{d(-x)}{dx} = -f'(x)\frac{dx}{dx}\\ \\-f'(-x) = -f'(x)\\\\f'(-x) = f'(x)[/tex]
Hence proved.
So, g'(-x) = g'(x)
⇒g'(-3) = g'(3) = 4
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