solve all 9 sub-problems. step-by-step handwritten solution. do not copy from anywhere.

Open-box Problem. An open-box (top open) is made from a rectangular material of dimensions a = 8 inches by b = 8 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. 19 X b 45 6 7 8 8 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 : V -T (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' =(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 endpoint is: (8) The maxim volume is V= (9) Answer the original question. The value of x that maximizes the volume is