(11) Let f(x) = x^3− 1 and g(x) = 2 + 5 sin 3x. (a) What is the range of g(f(x))? Justify your answer.
(b) If h(x) = f(g(x)) compute h′(x).
(c) If t(x) = e^f(x) compute t′(x). [6 marks]
(d) Obtain f′(x) from first principles. [6 marks]
(e) Obtain the equation of the line tangent to the curve y = f(x) at x = 3.

Ascientist has discovered an organism that produces five offspring exactly one hour after its own birth, and then goes on to live for one week without producing any additional offspring. each replicated organism also replicates at the same rate. at hour one, there is one organism. at hour two, there are five more organisms. how many total organisms are there at hour seven? 2,801 19,531 19,607 97.655