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

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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
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This note was uploaded on 03/30/2010 for the course MATH 11111 taught by Professor Stankova during the Fall '09 term at University of California, Berkeley.

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

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