Open-box Problem. An open-box (top open) is made from a rectangular material of dimensions a = 13 inches by b = 11 inches by cutting a square of side z at each corner and turning up the sides (see the...

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Extracted text: Open-box Problem. An open-box (top open) is made from a rectangular material of dimensions a = 13 inches by b = 11 inches by cutting a square of side z at each corner and turning up the sides (see the figure). Determine the value of r that results in a box the maximum %3D volume. %23 Following the steps to solve the problem. Check Show Answer only after you have tried hard. (1) Express the volume V as a function of r: V (2) Determine the domain of the function V of a (in interval form): (3) Expand the function V for easier differentiation: V = (4) Find the derivative of the function V: V'D


Extracted text: (3) Expand the function V for easier differentiation: V %3D (4) Find the derivative of the function V: V': %3D (5) Find the critical point(s) in the domain of V: (6) The value of V at the left endpoint is (7) The value of V at the right endpoint is (8) The maximum volume is V: (9) Answer the original question. The value of a that maximizes the volume is: