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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