QuestionAn open-top box is to be constructed from a 4 in by 10 in rectangular sheet of tin by cutting out squares of equal size at each corner, then folding up the resulting flaps. Let denote the length of the side of each cut-out square. Assume negligible thickness. (a) Find a formula for the volume, , of the box as a function of (b) For what values of 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)
Studdy Solution
To find the approximate maximum volume, calculate the derivative of the volume function and find its critical points within the interval . Then evaluate the volume at these critical points and endpoints to determine the maximum.
The approximate maximum volume of the box is found to be:
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