To answer this question efficiently we observe that, if a function h(x) is continuous and strictly decreasing on the interval (??, ?), then every relative maximum of a composite function h(g(t)) corresponds to the relative minimum of g(t), and vice versa.

(a) The derivative of h(x) = cot?1 x is given in Section 4.8 (p. 223) of the Course Notes. Use this to determine whether h(x) is strictly increasing on the interval (??, ?), or strictly decreasing on (?, ?), or neither.

(b) A poison was dumped into a pond, and within 10 days, most of the fish in the pond died. It was found that the population of fish, t days after the poisoning