Suppose that the temperature in Chicago, Illinois, in degrees Fahrenheit (F), can be modeled by a sinusoidal function C(t) where t is the time in months since January 1. Note that, for example, August 1 is seven months after January 1. The coldest day is January 1, at 24F, and the average temperature over the entire year is 52F.

1. Suppose that the temperature in Chicago, Illinois, in degrees Fahrenheit (F), can be modeled by a sinusoidal function C(t) where t is the time in months since January 1. Note that, for example, August 1 is seven months after January 1. The coldest day is January 1, at 24F, and the average temperature over the entire year is 52F. Assume that the function f(x) is continuous and differentiable on the interval (0,12). The following table gives some of the values for f(x). 1 2 3 4 5 8 9 11 6 0 10 -1 f(x) 2 3 4 6 4 -4 -4 2 = Finally, let h(q) be the function 9 h(q) 1+q2 (a) Let A(w) = C(w)f(w). Find an approximate value for A'(3). (b) Let B(z) = h(f(z)). Find an approximate value for B'(7). el (c) Let D(l): Find the exact value of D'(2). h(e) (d) The function C(t) is invertible on the interval (0,6). Let C-1 denote the inverse to C on this interval. Suppose that (C-1)/(38) = 0.08. Give a practical interpretation of this equation