Question

The graph of a function g is shown..... (a) Which of the following verifies that g satifies the hypotheses of the Mean Value Theorem on the interval [0,8]? (Select all that apply. □g is differentiable on the open interval (0,8) □g obtains at least one maximum on the closed interval [0,8]. □g takes only positive values on the closed interval [0,8] 0gis continuous on the closed interval [0,8] O g obtains at least one minimum on the open interval (0,8) O g is continuous on the open interval (0,8) (b) Estimate the value(s) of c that satisfy the conclusion of the Mean Value Theorem on the interval [0,8]. (Enter your answers as a comma-separated list. Round your answers to one decimal places. If an answer does not exist, enter DNE.) c= (c) Estimate the value(s) of c that satisfy the conclusion of the Mean Value Theorem on the interval [2,6]. (Enter your answers as a comma-separated list. Round your answers to one decimal places. If an answer does not exist, enter DNE.) c=

Answer 1

A. g is continuous on the closed interval [0,8]

g is differentiable on the open interval (0,8)

B. We can approximately say that c is 2.2 and 6.5

C. c is approximately 3.7 and 5.5 in this case

What is the mean value theorem?

The mean value theorem basically asserts that there is at least one place where the tangent to the arc is parallel to the secant through its ends for any given planar arc between two endpoints. One of the most significant findings in real analysis is this one.

Here, we have

A. Therefore, according to the theorem, the hypothesis for the mean value theorem for the given function must be

g is continuous on the closed interval [0,8]

g is differentiable on the open interval (0,8)

Hence, options fourth and sixth are rightly selected.

B. According to graph, f(0) = 1 and f(8) = 4

We will see this graphically, by first drawing the line joining the endpoints and then see is parallel lines where they intersect the graph

y = g(x) 0 1 2.2 6.5

Hence, we can approximately say that c is 2.2 and 6.5.

C. Similarly, we will do for the interval [2.6] as we did in part b), we get

y(x)  = 0 1 2 3.7 5.5 6

Hence, c is approximately 3.7 and 5.5 in this case

To learn more about the mean value theorem from the given link

brainly.com/question/29056690

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