Open-box Problem. An open-box (top open) is made from a rectangular material of dimensions a=12 inches by 10 inches by cutting a square of side x at each corner and turning up the sides (see the figure). Determine the value of x that results in a box the maximum volume. (1) Express the volume V as a function of x: V= 2) Determine the domain of the function V of x (in interval form): 3.) Expand the function V for easier differentiation: V=
Open-box Problem. An open-box (top open) is made from a rectangular material of dimensions a=12 inches by 10 inches by cutting a square of side x at each corner and turning up the sides (see the figure). Determine the value of x that results in a box the maximum volume.
(1) Express the volume V as a function of x: V=
2) Determine the domain of the function V of x (in interval form):
3.) Expand the function V for easier differentiation: V=
4.) Find the derivative of the function V: V'=
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 x that maximizes the volume is:
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