The given graph shows the temperature T in °F at Davis, CA, on April 18, 2008, between 6 a.m. and 6 p.m.

a. Estimate the rate of temperature change at the times

i) 7 a.m. 

ii) 9 a.m. 

iii) 2 p.m. 

iv) 4 p.m.

b. At what time does the temperature increase most rapidly? Decrease most rapidly? What is the rate for each of those times?

c. Use the graphical technique of Example 3 to graph the derivative of temperature T versus time t.

Example 3

Graph the derivative of the function y = ƒ(x) in Figure 3.6a.

In Figure 3.6a.

Temperature (F) 80 70 60 50 40 T 0 6 A.M. 3 9 A.M. 6 12 NOON Time (hr) 9 3 P.M. 12 6 P.M.