1. Section 4.3 Global Maxima and Minima Applied Calculus,4/E, Deborah Hughes-Hallett Copyright 2010 by John Wiley and Sons, All Rights Reserved

2. Applied Calculus,4/E, Deborah Hughes-Hallett Copyright 2010 by John Wiley and Sons, All Rights Reserved Figure 4.30: Global maximum and minimum on an interval domain, a ≤ x ≤ b Figure 4.31: Global maximum and minimum on the entire real line

3. Consider the graph of f(x) in the figure.

5. On the same side of a straight river are two towns, and the townspeople want to build a pumping station, S. See Figure 4.9. The pumping station is to be at the river’s edge with pipes extending straight to the two towns. Where should the pumping station be located so as to minimize the total length of the pipe? We need to minimize

6. t (hours since midnight)7891011 dH/dt ( ◦ F/hour)−5−10−2−4

7. Following a dose a of a drug, the average blood pressure of a patient is b. To compute the dose that maximizes the blood pressure, we (a) Find da/db and substitute b = 0. (b) Find db/da and substitute b = 0. (c) Solve for the values of a for which da/db = 0. (d) Solve for the values of a for which db/da = 0.

8. Applied Calculus,4/E, Deborah Hughes-Hallett Copyright 2010 by John Wiley and Sons, All Rights Reserved Problem 16 Figure 4.38 shows the rate at which photosynthesis is taking place in a leaf. (a) At what time, approximately, is photosynthesis proceeding fastest for t ≥ 0? 50 days (b) If the leaf grows at a rate proportional to the rate of photosynthesis, for what part of the interval 0 ≤ t ≤ 200 is the leaf growing? When is it growing fastest? t > 0 days; 50 days Figure 4.38