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# answers - Solutions to Some Practice Problems for the 1A...

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Solutions to Some Practice Problems for the 1A Final These are just answers so you can check that you did the problem correctly. For full credit on an exam you would need to show all your work. 1. x = 1000 ft, y = 1500 ft, make sure you check that this gives an ABSOLUTE minimum, and not just a local min. 2. 4000 cm 3 , again make sure this is an absolute max. 3. (1 , 3), verify that it is the absolute min. 4. x = 500, y = 125, check that this makes the product an absolute max. 5. V = πr 2 h + 2 3 πr 3 , and we want to minimize surface area which is SA = πr 2 +2 πrh +2 πr 2 , the answer is when r = ( 3 V 5 π ) 1 / 3 , and then solve for what h is also. You also need to check that this is an absolute minimum. 6. R ( x ) = xp ( x ) where p ( x ) = - 0 . 001 x + 23, for 0 x 15000 and R ( x ) is at an absolute maximum when x = 11500, so the price is p (11500) = \$11.50 7. x 3 = 4 5 8. 1 . 895494 9. Find f for the following (a) f = 1 2 x 2 + 25 9 · 14 x 14 / 5 + Cx + D (b) f = t 5 + 1 2 Cx 2 + Dx + E (c) f = 3 x 3 / 2 - 2 x 1 / 2 + 2 (d) f = 2 7 t 7 / 2 + 4 5 t 5 / 2 + C (e) f = 1 4 x 4 - 5 cos x + C 10.

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answers - Solutions to Some Practice Problems for the 1A...

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