Question

How do you find the instantaneous rate of change for `f(x)= x^3 -2x` for [0,4]?

Answer 1

A quick note on terminology: you cannot find the instantaneous rate of change over the interval `[0,4]`. You can, however, find the average rate of change over the interval, which is given by

`(f(4)-f(0))/(4-0)=(56-0)/4=14`

If you wanted to find the instantaneous rate of change at a point `x=a`, you would find `f'(a)`, where `f'(x)` is the function's derivative.