An open box is to be made out of a 10-inch by 16-inch piece of cardboard by cutting out squares of equal size from the four corners and bending up the sides. Find the dimensions of the resulting box that has the largest volume. Part 1: Find the volume of the open box as a function of x, where x represents the height of the open box. V (x) =

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 91E
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An open box is to be made out of a 10-inch by 16-inch piece of cardboard by cutting
out squares of equal size from the four corners and bending up the sides. Find the
dimensions of the resulting box that has the largest volume.
Part 1: Find the volume of the open box as a function of x, where x
represents the height of the open box.
V (x)
Part 2: Find the first derivative of the open box, with respect to X.
Part 3: Find the dimensions of the resulting box that has the largest volume.
Transcribed Image Text:An open box is to be made out of a 10-inch by 16-inch piece of cardboard by cutting out squares of equal size from the four corners and bending up the sides. Find the dimensions of the resulting box that has the largest volume. Part 1: Find the volume of the open box as a function of x, where x represents the height of the open box. V (x) Part 2: Find the first derivative of the open box, with respect to X. Part 3: Find the dimensions of the resulting box that has the largest volume.
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