# How do I find the maximum and minimum values of the function f(x) = x - 2 sin (x) on the interval [-pi/4, pi/2]?

Jan 30, 2015

You can derive your function and set your derivative equal to zero. The value(s) of $x$ you'll find will be the points of maxima or minima.

$f ' \left(x\right) = 1 - 2 \cos \left(x\right)$

Setting $f ' \left(x\right) = 0$ gives:

$1 - 2 \cos \left(x\right) = 0$
When $x = \frac{\pi}{3}$

You can now analyze when the derivative is bigger than zero:

$1 - 2 \cos \left(x\right) > 0$
i.e. when $x > \frac{\pi}{3}$

Your value of $x = \frac{\pi}{3}$ represent a minimum for your function, and in your interval you get the graph: