Concept explainers
Numerical, Graphical, and Analytic Analysis The cross sections of an irrigation canal are isosceles trapezoids of which three sides are 8 feet long (sec figure). Determine the angle of elevation 3 of the sides such that the area of the cross sections is a maximum by completing the following.
(a) Analytically complete six rows of a table such as the one below. (The first two rows are shown.)
0 |
Base 1 |
Base 2 |
Altitude |
Area |
10°ï¿½ |
8 |
|
|
|
20°ï¿½ |
8 |
|
|
|
(b) Use a graphing utility to generate additional rows of the table. Use the table to estimate the maximum cross-sectional area.
(c) Write the cross-sectional area 4 as a function of
(d) Use calculus to find the critical number of the function in part (c). Then find the angle that will yield the maximum cross-sectional area. What is the maximum area?
(e) Use a graphing utility to graph the function in part (c) and verify the maximum cross-sectional area.
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Calculus
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