The normal daily maximum temperatures T (in degrees Fahrenheit) for a certain city are shown in the table.

Question

Month	Jan	Feb	Mar	Apr	May	Jun	Jul	Aug	Sept	Oct	Nov	Dec
Temperature	31.0	35.3	46.6	59.0	70.0	79.7	84.1	81.9	74.8	62.3	48.2	34.8

(a)

Use a graphing utility to plot the data and find a model for the data of the form

T(t) = a + b sin(ct − d)

where T is the temperature and t is the time in months, with t = 1 corresponding to January. (Round all numerical values to two decimal places.)

T(t)=?

(c)

Find T ' and use a graphing utility to graph the derivative.

T'=?

Answer 1