# How do you find the maximum value of -3(sqrt(x-9) + 12)?

Jan 13, 2018

maximum value: $- 36$

#### Explanation:

You were probably intended to use derivatives, but here is a solution from a different approach.

Note that $\sqrt{x - 9} \ge 0$

$\Leftrightarrow \left(\sqrt{x - 9} + 12\right) \ge 12$

$\Leftrightarrow - 3 \left(\sqrt{x - 9} + 12\right) \le - 36$