Practice Quiz 3b

# Practice Quiz 3b - Practice Test IIIB for Math 1501...

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Practice Test IIIB for Math 1501, Calculus I I Let a and b be any two positive numbers such that a + b = 4 . (a) How large can ab 2 be? Find the values of a and b that make this as large as possible. (b) How large can ( 1 a + 1 b ) - 1 be? Find the values of a and b that make this as large as possible. II Let f be the function f ( x ) = p x 2 + 2 x - p x 2 + 2 for x > 0 . (a) Find all asymptotes of this function, if any. (b) Find all critical numbers for this function, if any. (c) For which values of x , if any, is this function increasing? (d) For which values of x , if any, is this function decreasing? (e) Does the function have an absolute maximum? III Use the Mean Value Theorem to answer the following questions. Let
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