You are constructing a closed box whose length, I, is three times its width, w, as indicated in the labels on the figure below. The mat (a) Write an equation for the volume of the box. 81 = 9w2 h 81 = 3wh? 81 = w2 h 81 = 3w2 h 81 = 9wh2 (b) Write an equation for the cost of the box in terms of w and h. C = 24wh + 18w² C = 12wh + 4w2 C = 24wh + 6w2 C = 12wh + 6w2 C = 24wh + 12w² OC = 6wh + 2w2 (c) Write an equation for the cost in terms of w only. Use lower case w. C(w) = (d) Find C '(w) = (e) Find the dimensions that minimize the cost of the box. W = inches h = inches

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.