## Practice Problems

### Problems

29. Find a point on the graph of so the tangent line to at goes through the origin.

31. Rumor. The percent of a population, , who have heard a rumor by time is often modeled for some positive constant A. Calculate how fast the rumor is spreading, .

In problems 33 – 41, find a function with the given derivative.

Problems 43 – 47 involve parametric equations.

43. At time minutes, robot is at and robot is at .

(a) Where is each robot when and ?

(b) Sketch the path each robot follows during the first minute.

(c) Find the slope of the tangent line, , to the path of each robot at minute.

(d) Find the speed of each robot at minute.

(e) Discuss the motion of a robot which follows the path for 20 minutes.

45. For the parametric graph in Fig. 9, determine whether and are positive, negative or zero when and .

(b) Find , the tangent slope , and speed when and .

(The graph of is called a cycloid and is the path of a light attached to the edge of a rolling wheel with radius ).

49. Describe the path of a robot whose location at time is

(c) Give the parametric equations so the robot will move along the same path as in part (a) but in the opposite direction.

Source: Dale Hoffman, https://s3.amazonaws.com/saylordotorg-resources/wwwresources/site/wp-content/uploads/2012/12/MA005-3.6-Some-Applications-of-the-Chain-Rule.pdf

This work is licensed under a Creative Commons Attribution 3.0 License.