2. The theorem Existence of Extrema on a Closed Interval guarantees that a continuous function on a closed interval takes on both a minimum and a maximum value on the interval. In such conditions those extrema values occur at critical points or endpoints of the interval. Given the function 12 x - 2, if - 4x < 6 5+6x- 2, f(x) if 6 x 8 TC a. Graph f(x) and explain why it does not fulfill the assumptions of the theorem Existence of Extrema on a Closed Interval on -4, 8 Will the extrema still exist? b. Find the critical points of f(x), then compare the values of f(x) at the critical points and the endpoints of -4, 8. What are the largest and smallest of these values? Is the smallest value found in b. the absolute minimum of f(x)? (Hint: compare with f(5.5)) d. Does f(x) have both extrema on -4, 8]? Why or why not? No it der nat
Transcribed Image Text:2. The theorem Existence of Extrema on a Closed Interval guarantees that
a continuous function on a closed interval takes on both a minimum and a
maximum value on the interval. In such conditions those extrema values occur
at critical points or endpoints of the interval.
Given the function
12 x - 2, if - 4x < 6
5+6x- 2,
f(x)
if 6 x 8
TC
a. Graph f(x) and explain why it does not fulfill the assumptions of the
theorem Existence of Extrema on a Closed Interval on -4, 8
Will the extrema still exist?
b. Find the critical points of f(x), then compare the values of f(x) at the
critical points and the endpoints of -4, 8. What are the largest and smallest
of these values?
Is the smallest value found in b. the absolute minimum of f(x)? (Hint:
compare with f(5.5))
d. Does f(x) have both extrema on -4, 8]? Why or why not?
No it der nat
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![2. The theorem Existence of Extrema on a Closed Interval guarantees that
a continuous function on a closed interval takes on both a minimum and a
maximum value on the interval. In such conditions those extrema values occur
at critical points or endpoints of the interval.
Given the function
12 x - 2, if - 4x < 6
5+6x- 2,
f(x)
if 6 x 8
TC
a. Graph f(x) and explain why it does not fulfill the assumptions of the
theorem Existence of Extrema on a Closed Interval on -4, 8
Will the extrema still exist?
b. Find the critical points of f(x), then compare the values of f(x) at the
critical points and the endpoints of -4, 8. What are the largest and smallest
of these values?
Is the smallest value found in b. the absolute minimum of f(x)? (Hint:
compare with f(5.5))
d. Does f(x) have both extrema on -4, 8]? Why or why not?
No it der nat](https://content.bartleby.com/qna-images/question/7b7b6a95-41e1-4624-b8d2-7e55c6545238/c6ab7035-3819-40e9-81fc-f66ef792ddb2/3z3ywqp.jpeg)
