A square sheet of metal of side 12 cm has a square of side cm cut from each corner. The sides are then folded up to form an open box. What is the maximum volume of the box?

Answer and explanation

Correct answer: B.

  1. Step 1: The base is by and the height is , so for .
  2. Step 2: , which is zero at in the domain.
  3. Step 3: at , a maximum, and .
Answer
.
Why not the others: is , which is not the maximum; and are not values of at its stationary point. Only gives a maximum.

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