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You are planning to make an open box from a 30- by 42 inch piece of sheet metal by cutting congruent squares from the corners and folding up the sides. You want the box to have the largest possible volume.

(a) What size square should you cut from each corner? (gice side length of square)

(b) What is the largest possible volume the box will have

I know [tex] V(x) = x(30-2x)(42-2x) [/tex]

So [tex] V'(x) = (30 - 2 x) (42 - 2 x) - 2 x (42 - 2 x) - 2 x (30 - 2 x) [/tex]

I find the critical points, however how do I find the maximum volume. Also I am not sure how you would find what square size you should cut. Shouldn't you find the maximum volume?

Thanks

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# Homework Help: Applied Maxima and Minima

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