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

Nov 30, 2015

Increasing.

#### Explanation:

Expand $f \left(x\right)$ to get ${x}^{3} - 2 {x}^{2} - 9 x + 18$
Differentiate to get
$3 {x}^{2} - 4 x - 9$
Insert $x = 3$ and you get $\mathrm{df} \frac{x}{\mathrm{dx}} = 6$

You have a positive value. Positive derivatives means increasing values.