Question

For what values of x does the graph of f have a horizontal tangent?
f(x) = x − 2 sin x

(Use n as your integer variable. Enter your answers as a comma-separated list.)

Answer 1

Horizontal tangents occur for values of \(x\) where the slope of the tangent line is zero.

This means you have to solve for all \(x\) that make
\[\begin{align*}f'(x)&=0\\
1-2\cos x&=0\end{align*}\]