Precal D Section 2.6

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Precal D Section 2.6

• Sample Problems

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Example 1 Maximum Area

• The perimeter of a rectangular region is 120 m.
• Write an equation for the area of the in terms of
  x, the length of one side.
• Find the maximum area.

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Example 2 Revenue and Demand

• The demand equation states the price p when x
  items are sold. The demand equation is p
  -.05x22.5
• Write an equation for the revenue as a function
  of x items sold.
• What price will produce the maximum revenue?

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Example 3 Pool Volume

• A swimming pool is 50 ft long and 25 ft wide. It
  is 12 ft deep at one end and 2 ft deep at the
  other end. The slope of the pool bottom is
  constant.
• Write an equation for the volume of water in the
  pool in terms of the depth of water in the deep
  end.
• What is the depth of the water if the volume is
  3000 cubic feet? 7500 cubic feet?

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Example 4 Distance

• A car leaves an intersection traveling east at 40
  mph. At the same time, a truck is 20 miles north
  of the intersection traveling south at 25 mph.
• Write an equation for the distance between the
  vehicles in terms of the time t.
• When does the minimum distance between the
  vehicles occur?

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Example 5 Box Volume

• An open box is to be constructed from a 15 in. x
  20 in. sheet of metal by removing a square from
  each corner and folding up the sides.
• Write an equation for the volume of the box in
  terms of the length of the cutout x.
• What dimensions will produce a box with maximum
  volume? What is the maximum volume?