You construct an open box with locking tabs from a square piece of material, 32 inches on a side, by cutting equal squares from thecorners and folding along the dashed lines (see figure, where M=32). Determine the length of the side x of the equal square at eachcorner that will maximize the volume of the resulting box.x=1in.(Round your answers to two decimal places, if necessary.)Complete the following parts.(a) Give a function f in the variable x for the quantity to be optimized.f(x)=(b) State the domain of this function. (Enter your answer using interval notation.)(c) To determine the optimal value of the function f, we need the critical numbers of(d) To find these critical numbers, we need to find=. (e) These critical numbers are as follows. (Round your answer(s) to two decimal places, if necessary. If a critical number is anendpoint of the domain, do NOT include it in your answer. Enter your answers as a comma-separated list. If an answer does not exist,enter DNE.)x=