Question

What is the instantaneous rate of change for `f(x)=x^3-x^2-2x 4` when x=2?

Answer 1

0

Explanation:

The instantaneous rate of change is the gradient of the slope at a given point, in this case, when `x=2`

The function is: `f(x)=x^{3}-x^{2}-8x`

The gradient function is: `f'(x)=3x^{2}-2x-8`

Let `x=2`

therefore the gradient of the curve at this point is

`f'(x)=3*4-2*2-8`
`f'(x)=12-4-8`
`f'(x)=0`