In interval <a, b> the average rate of change the function you count from this formula:
[tex]x=\frac{f(b)-f(a)}{b-a} \qquad b>a[/tex]
Here you've got a=-1 and b=1:
[tex]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= \frac{-1+11}{1+1}=\frac{10}{2}=5[/tex]
