Chapter 9.4, Problem 22E

Find the first partial derivative of the given function

Explain how a directional derivative is formed from the two partial derivatives ƒx and ƒy.

The graph shows how the average surface water temperature f of Lake Michigan varies over the course of a year (where t is measured in months with t = 0 corresponding to January 1). The average was calculated from data obtained over a 20-year period ending in 2011. fA (°F) 70 60+ 50- 40 4 6 8 10 12 t (months) Sketch the graph of the derivative function y = f'. y y y y 15 15 15 15 10 10 10 10 5 5 5. 5 t t 2 3 4 5 6 7 8 9 10 11 12 1 3 5 6 7/ 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 3 5 6 7 8 9 10 11 12 -5F -5 -5 -5 - 10 - 10 - 10 - 10 -15 - 15 - 15 - 15 When is f'(t) largest? t =