MATH 203 Exam 2, Spring 2008

arta Math 203 Time:55 min Quiz II : at Find the derivative of the following : ) Al fees 3) y= =p y ye 4+] dy= Vo 2) xy 3 =6-x* +2y 4) x+y -J2xy =0 A Find and classify all critical points ; I) y=f@)= > 2) y=2x+i 4) y =3x° -5x? / MD Given y =f (x)= x*- 18x? 1) Find and classify all the critical peints . 2) Sketch the graph . 3) Using the graph ,identify any absolute maximum or minimum. 4) State - the intervals over which f (x) is increasing , i - the intervals over which f (x) is decreasing . IV ).Determine the absolute maximum and the absolute minimum for the following functions over the given intervals x-2 . x? 3 , b) xy=5 5 l<xsih a oFind the equations of the tangent lines to the curve : x°-2x?y+y?=4 — atthe point x= _YI¥For a certain product ,the demand and anit price are related by : q= p’-40p +1250 O0<ps20 where p=The price of one unit ,in $ 3)y=4x? 3 ie ay y= OSxSZ q = The quantity demanded at p dp a) Find dq b) Evaluate q at p = 10, then interpret ; c) Evaluate ‘a , then interpret;