Engineering Board Exam Reviewer · Optimization (Maxima and Minima) · medium
An open-top box is made by cutting equal squares of side x from each corner of a 12 in by 12 in sheet of cardboard and folding up the sides. Find the value of x that maximizes the volume.
- 2 in
- 3 in
- 4 in
- 6 in
Answer
A. 2 in
Solution
V(x)=x(12-2x)2. V'(x)=(12-2x)2-4x(12-2x)=(12-2x)(12-6x). Setting V'=0 gives x=6 (rejected, gives zero volume) or x=2.
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