Open$-$box Problem. An open$-$box $($top open$)$ is made from a rectangular material of dimensions $\backslash ($ a$=9\backslash )$ inches by $\backslash ($ b$=8\backslash )$ inches by cutting a square of side $\backslash ($ x $\backslash )$ at each corner and turning up the sides $($see the figure$).$ Determine the value of $\backslash ($ x $\backslash )$ that results in a box the maximum volume. Following the steps to solve the problem. Check Show Answer only after you have tried hard. $(1)$ Express the volume $\backslash ($ V $\backslash )$ as a function of $\backslash ($ x: V$=\backslash )$