question
find the slope of the secant line between (x = - 2) and (x = 2) on the graph of the function (f(x)=5x^{3}-x^{2}-5x - 3).
provide your answer below:

Question

Accepted Answer

# Answer:
17
# Explanation:
## Step1: Find $f(-2)$
$$
\begin{align*}
f(-2)&=5(-2)^{3}-(-2)^{2}-5(-2)-3\
&=5\times(-8)-4 + 10-3\
&=-40-4 + 10-3\
&=-37
\end{align*}
$$
## Step2: Find $f(2)$
$$
\begin{align*}
f(2)&=5(2)^{3}-(2)^{2}-5(2)-3\
&=5\times8-4-10 - 3\
&=40-4-10-3\
&=23
\end{align*}
$$
## Step3: Calculate the slope of the secant line
The slope $m$ of the secant line between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here $x_1=-2,y_1 = f(-2)=-37,x_2 = 2,y_2=f(2)=23$.
$$
\begin{align*}
m&=\frac{f(2)-f(-2)}{2-(-2)}\
&=\frac{23-(-37)}{2 + 2}\
&=\frac{23 + 37}{4}\
&=\frac{60}{4}\
&=17
\end{align*}
$$

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QUESTION IMAGE

Question

Explanation:

Step1: Find \(f(-2)\)

Step2: Find \(f(2)\)

Step3: Calculate the slope of the secant line

Answer: