Question

Calculate the average rate of change for the function f(x) = x4 + 3x3 - 5x2 + 2x - 2, from x = -1 to x = 1

Answer 1

Workings and answer in the attachments below.

Answer 2

In interval <a, b> the average rate of change the function you count from this formula:

`x=(f(b)-f(a))/(b-a) \qquad b>a`
Here you've got a=-1 and b=1:

`f(a)=f(-1)=(-1)^4+3 \cdot (-1)^3 - 5 \cdot (-1)^2 +2 \cdot (-1)-2= \\ = 1-3-5-2-2=-11 \\ \\ f(b)=f(1)=1^4+3 \cdot 1^4 - 5 \cdot 1^2 + 2 \cdot 1 -2=1+3-5+2-2=-1 \\ \\ \hbox{So average rate of change this function is:} \\ \\ x= (-1+11)/(1+1)=(10)/(2)=5`