Math 160 Study Guide
Popular in Survey of Calculus
Popular in Math
This 4 page Study Guide was uploaded by Casey McConnell on Sunday March 6, 2016. The Study Guide belongs to 160 at Iowa State University taught by Dr. Michael Pollack in Spring 2016. Since its upload, it has received 120 views. For similar materials see Survey of Calculus in Math at Iowa State University.
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Date Created: 03/06/16
Name: Section: Math 160: Exam 2 No calculators allowed. Show all your work. p 0 1. (4 points) Let h(x) = 3x ▯ 2x + 1. Find h (x). 6 0 2. (4 points) Let f(x) = (3x + 1) (x ▯ 1). Find f (x) (Don’t need to simplify after taking derivative). 2 3. (4 points) Let g(x) = x + 5 . Find g (x). x ▯ 1 4. (9 points) A ladder 10 feet long is leaning against a building (as seen below). If the bottom of the ladder slides away horizontally from the building at a rate of 3 feet per second, how fast is the ladder sliding down the wall when the top of the ladder is 6 feet from the ground? 5. (5 points) Find dy for x y + 3y = x dx 4x + x 6. (5 points) Find the equations for the vertical and horizontal aymptotes for y = 2 x ▯ 9 3 2 7. Consider f(x) = ▯x ▯ 3x + 9x + 2. (a) (5 points) Find intervals of increasing and decreasing (b) (2 points) Find and label any relative extremum (if they exist). Only need x-value(s). 1 5 4 8. Consider f(x) = x + x . 5 (a) (5 points) Find intervals of concavity (b) (2 points) Find any in ection points (if they exist). Only need x-value(s). 9. (5 points) Use the following information to sketch the graph of f(x) Domain: (▯1;2) [ (2;1) Vertical Asymptote: x = 2, Horizontal Asymptote: y = 0 f(x) is increasing on (▯1;▯3) [ (0;2) [ (2;1), f(x) is decreasing on (▯3;0) f(x) is concave up on (▯1;▯3) [ (▯3;2), f(x) is concave down on (2;1) Relative max at (▯3;3), Relative min at (0;0)
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