You need to build a box from an 8 inch by 10 inch piece of carboard. To do this, you cut out squares of length x X from the four corners of the box in order to fold the sides up. (a) Verify that the volume of the box is given by the equation: 10 in V = 4x3 36x? + 80x (b) What is the largest value you can choose for x? What is the small- est value you can choose for x? Be sure to explain your reasoning completely. 8in (c) For what value of x will your box have the largest volume?