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Chapter 53: Q54.1-1ITD (page 1188)
Make a bar graph of the data in part 1. (For additional information about graphs, see the Scientific Skills Review in Appendix F and in the Study Area in Mastering Biology.)
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Explain why a constant per capita rate of growth (r) for a population produces a curve that is J-shaped.
46.\(f\left( x \right) = 36x + 3{x^2} - 2{x^3}\)
(a) Find the intervals of increase or decrease.
(b) Find the local maximum and minimum values.
(c) Find the intervals of concavity and the inflection points.
(d) Use the information from parts (a)鈥�(c) to sketch the graph.
You may want to check your work with a graphing calculator or computer.
58. \(S\left( x \right) = x - \sin x,{\rm{ 0}} \le x \le 4\pi \)
The observation that members of a population are uniformly distributed suggests that
(A) resources are distributed unevenly.
(B) the members of the population are competing for access to a resource.
(C) the members of the population are neither attracted to nor repelled by one another.
(D) the density of the population is low.
(a) Find the vertical and horizontal asymptotes.
(b) Find the intervals of increase or decrease.
(c) Find the local maximum and minimum values.
(d) Find the intervals of concavity and the inflection points.
(e) Use the information from parts (a)鈥�(d) to sketch the graph of f.
61. \(f\left( x \right) = {e^{{{ - 2} \mathord{\left/
{\vphantom {{ - 2} x}} \right.
\kern-\nulldelimiterspace} x}}}\)
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