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Unformatted text preview: SAMPLE MIDTERM II HINTS AND SOLUTIONS MATH 132 - WI01 1. For the function f ( x ) = x 2 e- x (a) use derivatives to determine the interval(s) (if any) on which f ( x ) is increasing and the interval(s) (if any) on which f ( x ) is decreasing (if there are none, please say so). (b) Use the information obtained in part (a) to find the values of x for which f ( x ) has relative max and relative min. (if there are none, please say so)). 2. Given that the points (0 , 0), (- 1 ,- 2), (2 , 1 . 6), (- 2 ,- 1 . 6), ( √ 3, √ 3), (- √ 3,- √ 3) all lie on the graph of y = f ( x ). From f ( x ) and f ”( x ) find where f is de- creasing, increasing, where f has rel max, rel. min, where f has points of inflection, where f is concave up, where f is concave down and sketch the graph roughly. f ( x ) =- 4( x- 1)( x + 1) ( x 2 + 1) 2 f 00 ( x ) = 8 x ( x- √ 3)( x + √ 3) ( x 2 + 1) 3 3. Find the critical points for y =- 1 3 + 8 x 2- 1 6 x 6 (a) classify them as rel max, rel min (b) find its points of inflection...
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