Question

question
find the slope of the secant line between x = -1 and x = 1 on the graph of the function f(x)=-x^3 - 3x^2 - 2x + 1.
provide your answer below:

Explanation:

Step1: Find $f(-1)$

Substitute $x = - 1$ into $f(x)$:
$f(-1)=-(-1)^{3}-3(-1)^{2}-2(-1)+1=1 - 3 + 2+1=1$

Step2: Find $f(1)$

Substitute $x = 1$ into $f(x)$:
$f(1)=-(1)^{3}-3(1)^{2}-2(1)+1=-1-3 - 2 + 1=-5$

Step3: Use the slope formula

The slope 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 $x_1=-1,y_1 = f(-1)=1,x_2 = 1,y_2=f(1)=-5$.
$m=\frac{f(1)-f(-1)}{1-(-1)}=\frac{-5 - 1}{1+1}=\frac{-6}{2}=-2$

Answer:

$-2$