m106_prelim2_v4_short - Prelim 2 V4 Math 1106 Please show your reasoning and all your work This is a 90 minute exam Calculators are not needed or

# m106_prelim2_v4_short - Prelim 2 V4 Math 1106 Please show...

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March 29, 2012 Prelim 2 V4 Math 1106 Please show your reasoning and all your work. This is a 90 minute exam. Calculators are not needed or permitted. Good luck! Unless specifically requested, answers on this exam NEED NOT be simplified or completely numerical. Arithmetic expressions are fine. Ordinarily, answers like ln 12 5 , 3 x 2 ( x 4 - 1) - 4 x 3 ( x 3 + 1) ( x 4 - 1) 2 , 1 2 ( 4 x 3 ) ( x 4 + 1) . 5 are completely acceptable. Problem 1) (20 Points) 1a) Evaluate x 3 - 6 x + 3 dx 1b) Evaluate x + 1 x 2 dx 1c) Evaluate t + 2 t 4 t 2 dt 1d)Use the method of substitution to evaluatex3sin (3x4+ 1)dx1e)Evaluatee4 Problem 2) (16 Points)For each of the following functions, find all criticalnumbers and use the second derivative test to classify them as relative (i.e.local) minima or maxima.2a)f(x) =x3-9x2+ 24x-16.2b)f(t) =t2e-t.Problem 3) (15 Points)For the functionf(x) =x3-3x: 1