# Math Help - differentiation application

1. ## differentiation application

Let f(x)=|sinx-1/2|. The maximum value attained by f is?

2. I don't know why you would need differentiation to help you solve this one but:

$-1 \leq \sin x \leq 1 \quad \mbox{Range of sin(x)}$
$-\frac{3}{2} \leq \sin x - \frac{1}{2} \leq \frac{1}{2} \quad \quad \mbox {Substract all sides by } \frac{1}{2}$

$\left| \sin x - \frac{1}{2} \right| \leq \frac{3}{2} \quad \quad \mbox {Voila}$