Question

Use the following graph of the function f(x) = 2x3 + x2 − 3x + 1 to answer this question: graph of 2x cubed plus x squared minus 3x plus 1 What is the average rate of change from x = −2 to x = 0?

Answer 1

Answer:

The average rate of change from x = −2 to x = 0 is 3.

Step-by-step explanation:

The given function is,

$f(x)=2x^3+x^2-3x+1$

Put x=-2,

$f(-2)=2(-2)^3+(-2)^2-3(-2)+1=-5$

Put x=0

$f(0)=2(0)^3+(0)^2-3(0)+1=-1$

From the graph of f(x) it is noticed that the graph passing through (-2,-5) and (0,2).

Average rate of change is the change is function with respect to x.

$m=\frac{f(x_2)-f(x_1)}{x_2-x_1}$

$m=\frac{f(0)-f(-2)}{0-(-2)}$

$m=\frac{1-(-5)}{2}$

$m=\frac{1+5}{2}$

$m=\frac{6}{2}$

$m=3$

Therefore the average rate of change from x = −2 to x = 0 is 3.