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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 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://prod-qna-question-images.s3.amazonaws.com/qna-images/question/7b7b6a95-41e1-4624-b8d2-7e55c6545238/8b61576b-943c-4074-851b-ebc5d99565a5/sjijto.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
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12+x-x, if -4sx<6 Consider the function as f(x) 5+6x-x, if 6sx8 In order to decide the existence of both extrema on the interval -4,8], take graphical method as shown below. (0.5,12.25) y 12+x-x, if-4sx<6 f(x)= 5+6x-, if 6sxs8 0+ 10 -5 5 x 10 (6,-18) 20
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