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Social Science2. The theorem Existence of Extrema on a Closed Interval guarantees thata continuous function on a closed interval takes on both a minimum and amaximum value on the interval. In such conditions those extrema values occurat critical points or endpoints of the interval.Given the function12 x - 2, if - 4x < 65+6x- 2,f(x)if 6 x 8TCa. Graph f(x) and explain why it does not fulfill the assumptions of thetheorem Existence of Extrema on a Closed Interval on -4, 8Will the extrema still exist?b. Find the critical points of f(x), then compare the values of f(x) at thecritical points and the endpoints of -4, 8. What are the largest and smallestof 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
Problem 2 part A, B, and C
![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://prod-qna-question-images.s3.amazonaws.com/qna-images/question/5e05de12-22ea-4048-b5b2-80f66e0dbea5/8d1e2441-a143-4214-b891-129025711794/eqxwl4d.jpeg)
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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
Expert Answer
As per norms, three aspects of the question are answered. It is adivisable post multiplie parts separately. The problem is concerned with continuity, local and global critical (extreme values) ,
part 1) graph of f(x) over the closed interval [-4,8]
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6.5) T
Part 2 )f(x) fails the continuity test at x=6, f(x) approaches -18 from the left and 5 (=f(6)) from the right...
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-0 6,5) -1e T
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Calculus
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