Math 121 - Chapter 6 Study Guide

1. Find the absolute maximum and minimum values of a function on a closed interval and state where those values occur. Look at problems 6.1.5-14*
2. Find the absolute maximum and minimum values, if any, of the function, over the set of all real numbers. Look at problems 6.1.15-20*
3. Find the absolute maximum and minimum values, if any, of the function, over the given interval. Two parts. Look at problems 6.1.23-34*
4. The position function of a particle is given. Find the velocity and acceleration functions; the position, velocity, speed, and acceleration at a specified time; when the particle is stopped; when the particle is speeding up and slowing down; and the total distance traveled over a time interval. Look at problems 6.3.11-14*
5. Applied minimum or maximum problem. Look at problems 6.2.42-45, 56-57*
6. Rectilinear motion problem involving the height of freely falling body. Look at problems 6.3.25-27.
7. Newton's method. Look at problems 6.4.5-14*
8. Verify the hypotheses of Rolle's Theorem are satisfied on the given interval and then find all the values that are guaranteed by the conclusion of the theorem. Look at problems 6.5.3-8*
9. Verify the hypotheses of the Mean Value Theorem are satisfied on the given interval and then find all the values that are guaranteed by the conclusion of the theorem. Look at problems 6.5.11-16*
10. Identify by inspection whether each of the functions will have an absolute minimum, absolute maximum, both, neither, or not enough information given. Six parts.
11. Find the point on the curve closest to the given point. Look at problems 6.2.51-52*

Notes:

• *'d problems are directly from the text.