The goal of this problem is to show that the function for) = 4f 3:: satisfies both of the conditions {the hypotheses) and the conclusion of the Mean Value Theorem for x in the interval [1, 4]. Verification o'i Hypotheses: Fill in the blanks to show that the hypotheses of the Mean Value Theorem are satisfied: for) is I on[l,4] and is I on(l,4). Note: The answer in each box should be one word Verification 01' the Conclusion: If the hypotheses of the Mean Value Theorem are satised. then there is at least one ( , c } in the interval (1, 4) for which r _ f(4) - ftl) f (c) 4 _ (1) . Verity that the conclusion of the Mean Value Theorem holds by computing f(4) fU) _ 4 (1) _ I Now nd r: in (1,4) so that f ' (c) equals the answer you just found. {For this problem there is only one correct value of c.) r: = 2 Note: On an exam you may be asked to state the Mean Value Theorem (i.e., it may not be given to you), and to verify that a given function satises the assumptions of the Mean Value Theorem