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Need some help I do not necessary want the answer but the process to get the answer, thank you.
Use the following graph of the function f(x) = 2x3 + x2 − 3x + 1 to answer this question:
What is the average rate of change from x = −2 to x = 0?

Respuesta :

Given function :[tex]f(x) = 2x^3 + x^2-3x + 1[/tex].

We need to find the average rate of change from x = −2 to x = 0.

Let us find the values of y-coordinates for x=-2 and x=0 for the given function on the graph.

[tex]f(-2) = 2(-2)^3 +(-2)^2-3(-2) + 1=-5[/tex]

[tex]f(0)=\:2\left(0\right)^3\:+\left(0\right)^2-3\left(0\right)\:+\:1 =1[/tex]

Formula for average rate of change is :

[tex]f_{avg}=\frac{f(b)-f(a)}{b-a}[/tex]

Plugging the values of f(a), f(b), a and b in the above formula, we get

[tex]f_{avg}=\frac{0-(-5)}{0-(-2)}  = \frac{5}{2}[/tex].

Therefore, the average rate of change from x = −2 to x = 0 is [tex]\frac{5}{2}[/tex].

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