Question

How do you find the average rate of change of `f(x) = x^4 + 3x^3 - 5x^2 + 2x - 2` over the interval [-1,1]?

Answer 1

5

Explanation:

The average rate of change of a function over an interval between 2 points (a ,f(a)) and (b ,f(b)) is

`color(red)(|bar(ul(color(white)(a/a)color(black)((f(b)-f(a))/(b-a))color(white)(a/a)|)))`

here the 2 points are (-1 ,f(-1)) and (1 ,f(1))

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

and `f(-1)=(-1)^4+3(-1)^3-5(-1)^2+2(-1)-2=-11`

`rArr(-1-(-11))/(1-(-1))=10/2=5`