The goal of this problem is to show that the function zc) :m2 2;1:3 3x+1 satises both the conditions (the hypotheses] and the conclusion of the Mean Value Theorem for :c) in the interval [4, 2]. Verification of Hypotheses: Fill in the blanks to show that the hypotheses of the Mean Value Theorem are satisfied: x) is continuous E on [4, 2] and is differentiable Z on (4, 2). Note: The answer in each box should be one word. Verification of the Conclusion: If the hypotheses of the Mean Value Theorem are satised: then there is at least one c in the interval [4, 2) for which I 7 f(_2)_f(_4) ftc)7_2_(_4) . Verify that the conclusion of the Mean Value Theorem holds by computing fti2} , f(*4) 2 (4) 2 2 Now find c in (4, 2} so that f'(c) equals the answer you just found. For this problem there is only one correct value of c. c : 2 Note: On an exam you may be asked to state the Mean Value Theorem tie, it may not be given to you), and to verify that a given function satisfies the assumptions of the Mean Value Theorem