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Taking this cue we dene f x 3x 1 at this point we have

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Unformatted text preview: → ∞. Readjusting the window, we find S does possess a relative minimum at x ≈ 12.60. As far as we can tell,4 this is the only relative extremum, and so it is the absolute minimum as well. This means the width and depth of the box should each measure approximately 12.60 centimeters. To determine the height, we find h(12.60) ≈ 6.30, so the height of the box should be approximately 6.30 centimeters. 4.3.1 Variation In many instances in the sciences, rational functions are encountered as a result of fundamental natural laws which are typically a result of assuming certain basic relationships between variables. These basic relationships are summarized in the definition below. Definition 4.4. Suppose x, y , and z are variable quantities. We say • y varies directly with (or is directly proportional to) x if there is a constant k such that y = kx. • y varies inversely with (or is inversely proportional to) x if there is a constant k such k that y = x . • z varies jointly with (or is jointly proportional to) x and y if there is a cons...
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