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 = −1 to x = 1?
−1
1
2
4

Answer 1

the answer to the question is 2

Answer 2

We have been given a polynomial
`f(x)=2x^(3) +x^(2)-3x+1` and we are asked to find average rate of change from x = −1 to x = 1.

First of all we will find f(-1) and f(1).

`f(-1)=2\cdot (-1)^(3) +(-1)^(2)-3(-1)+1`

`f(-1)=2\cdot (-1) +1+3+1`

`f(-1)=-2 +5=3`

Let us find f(1),

`f(1)=2\cdot (1)^(3) +(1)^(2)-3(1)+1`

`f(1)=2\cdot 1 +1-3+1`

`f(1)=2+1-3+1`

`f(1)=4-3=1`

Now let us find slope for our values.

`m=(y_2-y_1)/(x_2-x_1)`

`m=(f(1)-f(-1))/(1-(-1))`

`m=(1-3)/(1--1)`

`m=(-2)/(1+1)`

`m=(-2)/(2)=-1`

Therefore, average rate of change from our given x values will be -1.