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Meagan Clark

Meagan C.

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Consider the following problem: A box with an open top is to be constructed from a square piece of cardboard, $ 3 ft $ wide, by cutting out a square from each other of the four corners and bending up the sides. Find the largest volume that such a box can have.
(a) Draw several diagrams to illustrate the situation, some short boxes with large bases. Find the volumes of several such boxes. Does it appear that there is a maximum value? If so, estimate it.
(b) Draw a diagram illustrating the general situation. Introduce notation and label the diagram with your symbols.
(c) Write an expression for the volume.
(d) Use the given information to write an equation that relates the variables.
(e) Use part (d) to write the volume as a function of one variable.
(f) Finish solving the problem and compare the answer with your estimate in part (a).

Consider the following problem: A box with an open top is to be constructed from a square piece of cardboard, $ 3 ft $ wide, by cutting out a square from each other of the four corners and bending up the sides. Find the largest volume that such a box can have. (a) Draw several diagrams to illustrate the situation, some short boxes with large bases. Find the volumes of several such boxes. Does it appear that there is a maximum value? If so, estimate it. (b) Draw a diagram illustrating the general situation. Introduce notation and label the diagram with your symbols. (c) Write an expression for the volume. (d) Use the given information to write an equation that relates the variables. (e) Use part (d) to write the volume as a function of one variable. (f) Finish solving the problem and compare the answer with your estimate in part (a).

Calculus: Early Transcendentals

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ANSWERED

Alex Handzus verified

Numerade educator

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