Feb. 21, 2012Prelim 1 V3Math 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. Please note though that question 5 hasa specific alternate request.Problem 1) (20 Points)Find the following derivatives:1a)f(x) =x3-6x+ 31b)f(x) =x+1x1c)f(x) =xe3x4+11d)f(x) = lnx4+ 1x3-11e)f(x) = sin (x3-x)Problem 2 ) (12 Points)Joan invests $5000 in a bank account advertisingan interest rate of 6% per year.a)If the interest is compounded monthly, how much money will Joan haveafter 5 years?b)If the interest is instead just compounded annually, how long will it takefor the amount of money to triple?1