A sheet of cardboard is a square with each side 60 in length. The cardboard will...

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A sheet of cardboard is a square with each side 60" in length. The cardboard will be folded into a box with a lid, after four squares and two rectangular areas are removed (see diagram). What should x be to maximize the volume of the box? If you need help figuring out the dimensions of the box in terms of x, please come up and ask for help. 60 X X X 60 a) (2pts) Label the diagram completely with correct dimensions in terms of the variable x. 30-2x b) (3pts) What is the function (in terms of just x) that represents the volume of the box? c) (4pts) Find the value of x that maximizes the volume. d) (3pts) Explain how you know that you've found the correct maximum value using the first o second derivative test or the shape of the graph of the volume function. A sheet of cardboard is a square with each side 60" in length. The cardboard will be folded into a box with a lid, after four squares and two rectangular areas are removed (see diagram). What should x be to maximize the volume of the box? If you need help figuring out the dimensions of the box in terms of x, please come up and ask for help. 60 X X X 60 a) (2pts) Label the diagram completely with correct dimensions in terms of the variable x. 30-2x b) (3pts) What is the function (in terms of just x) that represents the volume of the box? c) (4pts) Find the value of x that maximizes the volume. d) (3pts) Explain how you know that you've found the correct maximum value using the first o second derivative test or the shape of the graph of the volume function.