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

a) The derivative of h(x)= cot^-1(x) is what. Use this to determine wheater h(x) is strictly increasing on the intervals (- infinite, infinite), or strictly decreasing on (infinite, infinite), or neither

b) A poison was dumbed 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 poisonning, was

f(t)=1000cot^-1(1/3t^3-7/2t^2+12t-13).

Find all the values of t E(0,10) at which f(t) has a relaitve maximum. Also find all t E(0,10) at which f(t) has a relative minimum.

Hint: I recomment using the second derivative method on g(x)=1/3t^3-7/2t^2+12t-13, and apply the above observation regarding compostie functions.

C) What are the horizontal asymptotes of the function y=f(t) (with domain (- infinite, infinite))?