An open box is to be made from a square piece of material, 36 centimeters on a side by cutting equal squares with sides of length x from the corners and turning up the sides (see figure). 36 - 2x (a) Determine which of the following functions V(x) represents the volume of the box. Ov(x) = x(36 - 2x)² Ov(x) = x²(36 - 2x)² Ov(x) = x²(36 - 2x) Ov(x) = (36 - 2x)² O v(x) = x(36 - 2x) (b) Determine the domain of the function V. 0 cm < x < 6 cm O x > 36 cm 0 cm < x < 18 cm. O x < 18 cm O 0 cm < x < 36 cm (c) Use the table feature of a graphing utility to create a table that shows various box heights x and the corresponding volumes V. (Fill in the table below.) Box Height, x Box Volume, V 1 cm cm³ cm3 cm3 2 cm 3 cm 4 cm 5 cm 6 cm 7 cm cm3 cm3 cm³ cm³ Use the table to estimate a range of dimensions within which the maximum volume is produced. The x-value is between 1 cm and 3 cm. The x-value is between 3 cm and 5 cm. The x-value is between 5 cm and 7 cm.

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