Using the definition of the derivative, find $f'(x)$. Then find $f'(-1)$, $f'(0)$, and $f'(3)$ when the derivative exists.
$f(x) = 5x^3 + 8$
To find the derivative, complete the limit as h approaches 0 for $
\lim_{h \to 0} \frac{f(x+h) - f(x)}{h}$
$\lim_{h \to 0} \frac{15x^2 + 15xh + 5h^2}{h}$
Find $f'(x)$ using the definition of the derivative.
$f'(x) = 15x^2$
Find $f'(-1)$ if the derivative exists. Select the correct choice below and, if necessary, fill in the answer box to complete your
A. $f'(-1) = 15$ (Simplify your answer.)
B. The derivative does not exist.
Find $f'(0)$ if the derivative exists. Select the correct choice below and, if necessary, fill in the answer box to complete your c
A. $f'(0) = $ (Simplify your answer.)
B. The derivative does not exist.