Question

How to find instantaneous rate of change for `f(x) = -x^4+1` at (3, -80)?

Answer 1

`f'(3)=-108`

Explanation:

The instant rate of change of a function `f` at `x=a` is given by `f'(a)`.

Here, `f(x)=-x^4+1`. The derivative of this is `f'(x)=-4x^3`. The instant rate of change of `f` at `x=3`, then, is `f'(3)=-4(3^3)=-108`.