Sketch the graph of the function and determine whether it has any absolute extreme values on its domain.
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A) no absolute maximum; no absolute minimum
B) no absolute maximum; absolute minimum at $x = \pi$
C) absolute maximum at $x = 0$; absolute minimum at $x = \pi$
D) absolute maximum at $x = 0$ and $x = 2 \pi$; absolute minimum at $x = \pi$

Question

Sketch the graph of the function and determine whether it has any absolute extreme values on its domain.
-

A) no absolute maximum; no absolute minimum 
B) no absolute maximum; absolute minimum at $x = \pi$ 
C) absolute maximum at $x = 0$; absolute minimum at $x = \pi$ 
D) absolute maximum at $x = 0$ and $x = 2 \pi$; absolute minimum at $x = \pi$

Quizplus · Accepted Answer

The graph is a cosine function, which oscillates between -1 and 1. Since there is no upper bound on the function, there is no absolute maximum. However, there is a lower bound of -1, which is achieved at $x = \pi$, so there is an absolute minimum at that point.

Sketch the Graph of the Function and Determine Whether It x=πx = \pix=π

Sketch the Graph of the Function and Determine Whether It $x = \pi$