Math 1325 Professor Merrill Lab 2 Name ____________________________________ Show all work Circle Answers Due Wed., Oct 7, 2009 1. The graph of f(x) is shown as follows: a. On what intervals is f increasing? b. on what intervals is f decreasing? c. At what point(s) does f has a local minimum? f. On what intervals is f concaves upward? d. At what point(s) does f has a local maximum? g. State the point(s) of inflection. e. On what intervals is f concaves downward? 3 2 2. A particle moves according to a law of motion s t 12t 36t , t 0 , where t is measured in seconds and s in meters. a. Find the velocity function v at time t. d. Find the points of inflection. b. Find the critical numbers. e. When in the particle at rest? c. Find the acceleration function a at time t. f. When in the particle is moving forward and when the particle is moving backward? Fall 2009 1 h. Draw a graph for all three functions s, v, and a. g. Find the total distance traveled during the first 8 seconds. i. When is the particle slowing down? j. When is the particle speeding up? 1 3. A ball is thrown upward with an initial velocity of 66 ft/s. s(t) t2 v0 t 2 a. Find an equation of the position of the ball in terms of time t. b. Sketch a graph of the position function. c. Find the velocity of the ball after 3 seconds. 4. Suppose that f (x) 1 2x 1 2x . Find f ( x) . Fall, 2009 2 5. Suppose that f (x) 2x 1 . Find f ( x) . 2x 1 6. If f (x) ln(3x 2 x 5)4 , find f (x). Write your answer in simplest form. 4 2 7. If f (x) e x x 4 , find f (x). Write your answer in simplest form. 8. If f (x) 3x(x3 4)6 , find f (x) . Write your answer in simplest form. Fall, 2009 3 9. If f (x) (3x 3x 2 )3 (2x x 2 )5 , find f (x) . Write your answer in simplest form. 4 2x x 2 10. If f (x) , find f (x) . Write your answer in simplest form. 3x x 3 Fall, 2009 4