Question

Using the graph of `f(x) = 2x^3 + x^2 - 3x+1`, what is the average rate of change from `x=-2` to `x=0`?

Answer 1

`3`

Explanation:

average rate of change on `x=-2` to `x=0` is:
`(f(0)-f(-2))/(0-(-2))`
`=((2(0)^3+(0)^2-3(0)+1)-(2(-2)^3+(-2)^2-3(-2)+1))/2`
`=(1-(-5))/2`
`=3`

graph{2x^3+x^2-3x+1 [-10, 10, -7, 7]}
the graph of `f(x)` passes through points `(-2,-5)` and `(0,1)`

the slope of the line passing through those two points is the average rate of change.