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Suppose a tin box is to be constructed with a square base, an open top and...

Suppose a tin box is to be constructed with a square base, an open top and a volume of 32 cubic inches. The cost of the tin to construct the box is $0.15 per square inch for the sides and $0.30 per square inch for the base.

1. The minimized cost of the tin box is A. $4.82 B. $3.50 C. $0 D. $9.07 E. none of the other answers

2. The cost is minimized at critical point x=a because the first derivative test found that

  • A.

    ?″(?)>0

  • B.

    ?′(?)=0

  • C.

    ?′(?) was negative to the left of x=a and positive to the right

  • D.

    ?′(?) was positive to the left of x=a and negative to the right

  • E.

    ?″(?)<0

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