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

Question

Quizplus · Accepted Answer

To find horizontal tangents, we set the derivative of the function equal to zero. The derivative of $y = \tan x - x$ is $y' = \sec^2 x - 1$. Setting $y' = 0$ gives $\sec^2 x = 1$, or $\cos^2 x = 1$, which occurs at $x = 0, \pi, 2\pi$ within the given interval.

Solve the Problem y=tan⁡x−xy = \tan x - xy=tanx−x Have Any Horizontal Tangents in the Interval

Solve the Problem $y = \tan x - x$ Have Any Horizontal Tangents in the Interval