Question

What is the instantaneous rate of change of `f(x)=(x-1)^2-4x` at `x=0`?

Answer 1

Instantaneous rate of change at x=0 of f(x) is -6.

Explanation:

`f(x)=(x-1)^2-4x`
`f(x)=x^2-2x+1-4x`
`f(x)=x^2-6x+1`

Use power rule to find `f'(x)`:
`f'(x)=2x-6`
`f'(0)=2(0)-6=-6`

`f'(0)=-6`