Practice Test IIIC for Calculus I, Math1501 I Consider the function f ( x )where f ( x )=5(1-e-x ) . (a) On the interval 3 ≤ x ≤ 5, is f increasing, decreasing, or neither? (b) On the interval 3 ≤ x ≤ 5, is f0 increasing, decreasing, or neither? (c) What is the largest value of | f0 ( x ) | on the interval 3 ≤ x ≤ 5 (d) Using the Mean Value Theorem, ﬁnd a number C so that | f ( x )-f ( y ) |≤ C | x-y | , for all 3 ≤ x, y ≤ 5 II Let f be the function given by f ( x )=(cos x ) 2 (1-sin x ) . (a) Find all the local extrema, i.e., all the local maxima and local minima. (b) Find the (global) maximum and minimum values
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