?Numerical, Graphical, and Analytic Analysis An open box of maximum volume is to be made from a square piece of material,24 inches on a side,by cutting
Chapter 4, Problem 2(choose chapter or problem)
Numerical, Graphical, and Analytic Analysis An open box of maximum volume is to be made from a square piece of material,24 inches on a side,by cutting equal squares from the corners and turning up the sides (see figure).
(a) Analytically complete six rows of a table such as the one below. (The first two rows are shown.) Use the table to guess the maximum volume.
(b) Write the volume V as a function of x.
(c) Use calculus to find the critical number of the function in part (b) and find the maximum value.
(d) Use a graphing utility to graph the function in part (b) and verify the maximum volume from the graph.
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