Question

given the function $f(x)=2x^{5}-3x^{3}$, determine the derivative of $f$ at $x = - 7$ using the limit shown below. you do not have to simplify your answer.
answer attempt 1 out of 2
$lim_{h
ightarrow0}$

Explanation:

Step1: Recall derivative limit - definition

The derivative of a function $y = f(x)$ at $x=a$ is given by $f^{\prime}(a)=\lim_{h
ightarrow0}\frac{f(a + h)-f(a)}{h}$. Here, $a=-7$ and $f(x)=2x^{5}-3x^{3}$.

Step2: Find $f(a + h)$ and $f(a)$

First, find $f(-7 + h)=2(-7 + h)^{5}-3(-7 + h)^{3}$. And $f(-7)=2(-7)^{5}-3(-7)^{3}$.

Step3: Substitute into the limit - formula

The derivative $f^{\prime}(-7)=\lim_{h
ightarrow0}\frac{2(-7 + h)^{5}-3(-7 + h)^{3}-(2(-7)^{5}-3(-7)^{3})}{h}$.

Answer:

$\lim_{h
ightarrow0}\frac{2(-7 + h)^{5}-3(-7 + h)^{3}-(2(-7)^{5}-3(-7)^{3})}{h}$