Question

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

Explanation:

Step1: Find $f(-1)$

$f(-1)=-2(-1)^{3}+3=-2\times(-1)+3 = 2 + 3=5$

Step2: Find $f(2)$

$f(2)=-2(2)^{3}+3=-2\times8 + 3=-16 + 3=-13$

Step3: Calculate the slope

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 $x_1=-1,y_1 = f(-1)=5,x_2 = 2,y_2=f(2)=-13$. So $m=\frac{-13 - 5}{2-(-1)}=\frac{-18}{3}=-6$

Answer:

-6