Question

The graph of a function f is shown. Does f satisfy the hypotheses of the Mean Value Theorem on the interval [0, 5]? If so, find a value c that satisfies the conclusion of the Mean Value Theorem on that interval. (If an answer does not exist,enter DNE.) a) Yes, because f is continuous on the open interval (0, 5) and differentiable on the closed interval [0,5]. b) Yes, because f is continuous on the closed interval [0, 5] and differentiable on the open interval (0, 5). c) Yes, because f is increasing on closed interval [0, 5]. d) No, because f does not have a minimum nor a maximum on the closed interval [0, 5]. e) No, because f is not differentiable on the open interval (0, 5). f) No, because f is not continuous on the open interval (0, 5).

Fig: 1

Fig: 2

Fig: 3

Fig: 4

Fig: 5