4.3A rectangular sheet of metal having dimensions 25 m and 15 m has squares removed from each of the four corners and folding the resulting flaps into a vertical position along the dotted lines to form an open box as shown in Fig. 6.3 below. Determine using differential calculus:

(a) the value of x, which will make the volume of the finished box to be as large as

possible.

(b) Confirm the validity of the value in (a)

(c) the final dimensions of the box

(d)the maximum volume

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