Unformatted text preview: function of x and state the applied domain.
5. Use a calculator to approximate (to two decimal places) the dimensions of the box which
minimize the surface area.
2 In this case, long division amounts to term-by-term division. 4.3 Rational Inequalities and Applications 271 Solution.
1. We are told the volume of the box is 1000 cubic centimeters and that x represents the width,
in centimeters. From geometry, we know Volume = width × height × depth. Since the base
of the box is to be a square, the width and the depth are both x centimeters. Using h for the
height, we have 1000 = x2 h, so that h = 1000 . Using function notation,3 h(x) = 1000 As for
the applied domain, in order for there to be a box at all, x > 0, and since every such choice
of x will return a positive number for the height h we have no other restrictions and conclude
our domain is (0, ∞).
2. To solve h(x) ≥ x, we proceed as before and collect all nonzero terms on one side of the
inequality and use a sign diagram.
h(x) ≥ x
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