Please complete the problem thoroughly and legibly!â
. Mean Value Theorem Look up the full statement of the Mean Value Theorem on the interwebs. It should be nice and "mathy". Write down precisely the full statement of the Mean Value Theorem. a. b. Carefully explain in sentences what the Mean Value Theorem is stating. It may help to draw a picture or graph to assist your explanation. Draw a continuous graph where the Mean Value Theorem does not work, despite the graph being continuous. Explain why the Mean Value Theorem fails on this graph. c. d. Hot water is dripping through a coffeemaker, filling a large cup with coffee. The amount of coffee in the cup at time t is given by a differentiable function C, where t is measured in minutes. Selected values of C(t) are given in the table below. Based on this information, is there a time t, 2 t 4, such that C'(t) = 2? Explain. 0 (minutes) C(t) (ounces) 0 5.38.8 11.2 12.8 13.8 14.5