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.?????????

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.?????????

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Rational Functions And Conics

Section4.2: Graphs Of Rational Functions

Problem 79E

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Question

An open box is to be made out of a 6-inch by 14-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.?????????

Expert Solution