Find the points at which the given function has slope zero

by RoRi

September 16, 2015

Consider the function

$f(x) = x + \sin x.$

Find the points $x$ at which the graph of $f$ at $(x,f(x))$ has slope zero.

First, the derivative is given by

$f'(x) = 1 + \cos x.$

Then, the requirement that the graph of $f$ has slope zero at $(x, f(x))$ is asking for the points at which $f'(x) = 0$ . So, we solve,

$f'(x) = 0 \ \implies \ 1 + \cos x = 0 \ \implies \ \cos x = -1 \ \implies \ x = (2n+1) \pi \quad n \in \mathbb{Z}.$

Stumbling Robot