Question

Is `f(x)=-4x^3+4x^2+2x-1` increasing or decreasing at `x=2`?

Answer 1

It is decreasing.

Explanation:

Start by deriving the function `f`, as the derivative function,`f'` describes the rate of change of `f`.

`f(x)=-4x^3+4x^2+2x-1`

`f'(x)=-12x^2+8x+2`

Then plug in `x=2` into the function.

`f'(2)=-12(4)+8(2)+2`

`f'(2)=-48+18`

`f´(2)=-30`

Hence, as the value of the derivative is negative, the instantaneous rate of change at this point is negative- so the function of `f` is decreasing in this instance.