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March 29, 2012Prelim 2 V4Math 1106Please show your reasoning and all your work.This is a 90 minuteexam. Calculators are not needed or permitted. Good luck!Unless specifically requested, answers on this exam NEED NOTbe simplified or completely numerical. Arithmetic expressions arefine. Ordinarily, answers likeln125,3x2(x4-1)-4x3(x3+ 1)(x4-1)2,12(4x3)(x4+ 1).5are completely acceptable.Problem 1) (20 Points)1a)Evaluatex3-6x+ 3dx1b)Evaluatex+1x2dx1c)Evaluate√t+ 2t4t2dt1d)Use the method of substitution to evaluatex3sin (3x4+ 1)dx1e)Evaluatee4Problem 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