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Unformatted text preview: MIDTERM EXAM CALCULUS FOR THE SOCIALANDMANAGEMENTSCIENCES Math 52-10 Spring 2008 There are 9 problems in all; together they are worth 110%; the value of each, as a per- centage, is denoted. Youmay choose to do any, or all, of these problems. Please be clear and precise in your solutions; I recommend that you display all your working. Do not return this exam paper; write all your solutions in the blue books provided. 1. The following is the graph of a function y = f(x), useit to determine: (a) The sign-chart of the functiony = f(x) (b) The sign-chart of the derivative y' = f'(x) (c) The sign-chart of the second derivative y" = f" (x) )~ ( (- ') )- ) '\- 6)-") (- 8 y~ )- J Do not provide any explanation I ~ 15% d(.---, l(-S)_') continued ... 1 2 h f . x(x-l)2 h d . . . , (x-l)(x+ 1)(4x-l) th o . I ave a unctIOn y = 2x+ 1 w ose envatlve IS y = /_. .," ; use IS information to determine: (a) The horizontal and vertical asymptotes of y (b) The x and y intercepts of y (c) The sign-chart ofy (d) The equation of the tangent to y at x =-2 (e) The sign-chart ofy' (f) The location (x and y coordinates) and type of each stationary point of y Draw a small diagram to denote the type of each SP; do not offer any explanation and do not sketch the graph 15% 3. Sketch the graph of any function y = f(x) with the following characteristics: . Holes atx =-1 and x = 6 . Horizontal asymptote at y =- 2....
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This note was uploaded on 04/19/2008 for the course MATH 52 taught by Professor Moses during the Spring '08 term at GWU.
- Spring '08