Problem 2 Part D
![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-b8d2-7e55c6545238/8b61576b-943c-4074-851b-ebc5d99565a5/sjijto.jpeg)
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