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

Apr 27, 2018

It is decreasing.

#### Explanation:

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

$f \left(x\right) = - 4 {x}^{3} + 4 {x}^{2} + 2 x - 1$

$f ' \left(x\right) = - 12 {x}^{2} + 8 x + 2$

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

$f ' \left(2\right) = - 12 \left(4\right) + 8 \left(2\right) + 2$

$f ' \left(2\right) = - 48 + 18$

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.