# What are the extrema of f(x)= x+sinx in [-pi,pi] ?

Nov 5, 2015

Absolute maximum at $\pi$ and an absolute minimum at $- \pi$.

#### Explanation:

For absolute extrema, we need to find the critical numbers by setting the derivative of the equation equal to 0 and plugging them into the function, and then plug in the endpoints of the interval into the original equation.

1. Finding the critical numbers
$f ' \left(x\right) = 1 + \cos x$
$1 + \cos x = 0$
$\cos x = - 1$
$x = \pi$ <-- critical number
$f \left(\pi\right) = \pi$

2. Plug in the endpoints
$f \left(- \pi\right) = - \pi$
$f \left(\pi\right) = \pi$

Comparing the three, we find that we have an absolute maximum at $\pi$ and an absolute minimum at $- \pi$.