Solve the problem.
-Does the graph of the function $y = 2 x + 4 \sin x$ have any horizontal tangents in the interval $0 \leq x \leq 2 \pi$ ? If so, where?
A) Yes, at $x = \frac { 2 \pi } { 3 }$
B) Yes, at $x = \frac { \pi } { 3 } , x = \frac { 2 \pi } { 3 }$
C) $\mathrm { No }$
D) Yes, at $x = \frac { 2 \pi } { 3 } , x = \frac { 4 \pi } { 3 }$

Question

Quizplus · Accepted Answer

The derivative of the given function is 
\begin{align*}
\frac{dy}{dx} &= 2+4\cos x,
\end{align*}
which is zero when $\cos x = -\frac{1}{2}$. Thus, the function has horizontal tangents when $\cos x = -\frac{1}{2}$, i.e. at $x = \frac{2\pi}{3}$ and $x=\frac{4\pi}{3}$ in the interval $0\leq x \leq 2\pi$. Therefore, the correct answer is $\boxed{	ext{(D)}}$.

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