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Unformatted text preview: 1. Find the absolute maximum and minimum values of the function h ( x ) = x 3- 3 x 2- 9 x + 19 on the interval [1 , 4]. Show all reasoning. 2. Consider the function g ( x ) = x 3 25- x 2 . (a) Find all critical numbers of g . (b) For each critical number c , determine whether the point ( c, g ( c )) on the graph of g is a local maximum, local minimum, or neither. Explain your reasoning. 3. Consider the function f , whose formula and derivatives are given below: f ( x ) = x 3 + x 2 f ( x ) = 3- x 2 (3 + x 2 ) 2 f 00 ( x ) = 2 x ( x 2- 9) (3 + x 2 ) 3 (a) Find the coordinates of all points, if any, where the graph of f crosses the x-axis. (b) Find equations for all of the vertical and horizontal asymptotes of this function, or state why there are none. (Justify asymptotes with limit calculations.) (c) Determine f s intervals of increasing and decreasing, and the coordinates ( x, f ( x )) of any local extrema, giving complete justification....
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