Question

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

Answer 1

`34`

Explanation:

Average rate of change may be given by `m=(Deltay)/(Deltax)`

So in this case, when x changes from -4 to -3, y changes from f(-4) to f(-3).

But `f(-4)=(-4)^3-3(-4)+5=-47`

Similarly `f(-3)=(-3)^3-3(-3)+5=-13`

Thus average rate of change (average gradient or slope) between these two points is
`m=(Deltay)/(Deltax)=(-13-(-47))/(-3-(-4))=34`