Figure 2 shows a rectangular sheet of metal which is 120 cm long and 90 cm...

  

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Figure 2 shows a rectangular sheet of metal which is 120 cm long and 90 cm wide. A square of side x cm is cut from two corners as shown in the diagram and the sides are then folded up to make a tray which is open at one end. a) Show that the volume of the tray, V, is given by V = 2x-330x + 10800x. b) Use calculus to find the value of x which gives the maximum volume. c) Use calculus to confirm your value of x gives a maximum. x cm x cm. 120 cm Figure 2 90 cm Figure 2 shows a rectangular sheet of metal which is 120 cm long and 90 cm wide. A square of side x cm is cut from two corners as shown in the diagram and the sides are then folded up to make a tray which is open at one end. a) Show that the volume of the tray, V, is given by V = 2x-330x + 10800x. b) Use calculus to find the value of x which gives the maximum volume. c) Use calculus to confirm your value of x gives a maximum. x cm x cm. 120 cm Figure 2 90 cm