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

question 175

Multiple Choice

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 \(x = 0 , x = \pi , x = 2 \pi\)

---

Definitions:

Referential Style

A language learning approach in which individuals predominantly use language to refer to people and objects in their environment.

Holophrasing

The use of a single word by a child to express a complex idea or complete thought, typical in early language development.

Prelinguistic Communication

Communication through sounds, facial expressions, gestures, imitation, and other nonlinguistic means.

Cooing

Early vocalization of infants that involves the production of soft, murmuring sounds, typically occurring between 2 to 4 months of age.