MATH 1712: WEEK 7

Topics for this week are:

• Optimization
• Exponential Functions and Their Derivatives

Objectives for this week:

• Calculate the absolute maximum and/or minimum value of a function on a closed interval
• Use the first- and second-derivative tests to solve optimization problems
• Sketch the graphs of exponential functions
• Find the derivative of expressions that include exponential functions

Text coverage:     Sections 4.4 - 4.5, 5.1, 5.4 of S. Tan.

Online resources:

• Week 7 Formula Sheet
• Week 7 Practice Problems
• Maple Worksheets
  • Finding Absolute Extrema:  This worksheet introduces all the Maple commands necessary to find the absolute maximum or minimum of a continuous function on a closed interval.
  • Maximum Heart-Rate for a Runner: The heart's pulse-rate for a well-trained runner will increase at the beginning of a run, and then decrease as the runner experiences a "second wind." There after, the pulse-rate will gradually increase as the runner switches from metabolizing glycogen to converting fat into an energy source. This toy model mimics this phenomena. It asks when the maximum heart rate will occur. The answer is obtained with the standard tool: set the derivative equal to zero and solve. It may be that the "solving" is the most interesting part from the perspective of computing in this worksheet.

---

Last Modified: . School of Mathematics, Georgia Institute of Technology.