Question

Select all of the following functions for which the extreme value theorem guarantees the existence of an absolute maximum and minimum. Select all that apply: $f(x) = \sin(\frac{\pi x}{2})$ over $[-1, 1]$ $g(x) = \frac{1}{\sin(\frac{\pi x}{2})}$ over $[\frac{1}{2}, \frac{3}{2}]$ $h(x) = \cos(\frac{\pi x}{2})$ over $[-1, 1]$ $k(x) = \frac{1}{\cos(\frac{\pi x}{2})}$ over $[\frac{1}{2}, \frac{3}{2}]$ None of the above.

          Select all of the following functions for which the extreme value theorem guarantees the existence of an absolute maximum and minimum.
Select all that apply:
$f(x) = \sin(\frac{\pi x}{2})$ over $[-1, 1]$
$g(x) = \frac{1}{\sin(\frac{\pi x}{2})}$ over $[\frac{1}{2}, \frac{3}{2}]$
$h(x) = \cos(\frac{\pi x}{2})$ over $[-1, 1]$
$k(x) = \frac{1}{\cos(\frac{\pi x}{2})}$ over $[\frac{1}{2}, \frac{3}{2}]$
None of the above.

Select all of the following functions for which the extreme value theorem guarantees the existence of an absolute maximum and minimum.
Select all that apply:
f(x) = sin((π x)/(2)) over [-1, 1]
g(x) = (1)/(sin((π x)/(2))) over [(1)/(2), (3)/(2)]
h(x) = cos((π x)/(2)) over [-1, 1]
k(x) = (1)/(cos((π x)/(2))) over [(1)/(2), (3)/(2)]
None of the above.

Added by Jennifer A.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Andrew Noble

07/31/2023

Step 1

Step 1: The extreme value theorem states that if a function is continuous on a closed interval, then it must have an absolute maximum and minimum on that interval. Show more…

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Texts: Select all of the following functions for which the extreme value theorem guarantees the existence of an absolute maximum and minimum. Select all that apply: f(x) = sin(x) over [-1,1] g(x) = sin(13) h(x) = cos(x) over [-1,1] k(x) over [,3] E(x) None of the above