An open-top box is to be constructed from a 4 in by 16 in rectangular sheet of tin by cutting out squares of equal size at each corner, then folding up the resulting flaps. Let a denote the length of the side of each cut-out square. Assume negligible thickness. (a) Find a formula for the volume, V, of the box as a function of x. V(x) = (b) For what values of a does the formula from part (a) make sense in the context of the problem? help (inequalities) (c) On a separate piece of paper, sketch a graph of the volume function. (d) What, approximately, is the maximum volume of the box? (include units: help (units))
An open-top box is to be constructed from a 4 in by 16 in rectangular sheet of tin by cutting out squares of equal size at each corner, then folding up the resulting flaps. Let a denote the length of the side of each cut-out square. Assume negligible thickness. (a) Find a formula for the volume, V, of the box as a function of x. V(x) = (b) For what values of a does the formula from part (a) make sense in the context of the problem? help (inequalities) (c) On a separate piece of paper, sketch a graph of the volume function. (d) What, approximately, is the maximum volume of the box? (include units: help (units))
Chapter3: Polynomial Functions
Section3.4: Zeros Of Polynomial Functions
Problem 9ECP
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