Math 220 March 7 I. If 1200 cm2 of material is available to make a ...

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$Math 220 October 30 I. Find f 1. f (x) = x √ x2 + sin(x) + cos(x), f(0 ...$

$Math Times - Mathematics - University of Illinois at Urbana-Champaign$

A ′′ (x) = 1600x −3 > 0 C = 4x + 2y C(x) = 4x + 800 x C ′ (x) = 4 − 800x −2 0 = 4 − 800x −2 x = 4x 2 − 800 200 = x 2 x = ± √ 200 There is maximum at x = √ 200 Cost is be minimize if the fence is built to be √ 200 by 2 √ 200 where √ 200 is the length of the 4 parallel sections. V. A Frisbee has landed in the ocean 150 from the shore. A dog is standing 200 feet down the shore from where the Frisbee landed. The dog can run 5 feet per second and swim 2 feet per second. How far should the dog run down the shore before he get jumps in the water to get the Frisbee in the least amount of time? Answer: T ime = 1 1 (x) + 1502 + (200 − x) 2 5 2 6
T (x) = 1 5 T ′ (x) = 1 5 + 1 (x) + 1502 + (200 − x) 2 2 −400 + 2x 4 1502 + (200 − x) 2 0 = 1 5 + −400 + 2x 4 1502 + (200 − x) 2 1 5 = 400 − 2x 4 1502 + (200 − x) 2 ( 1 5 )2 400 − 2x = ( 4 1502 )2 + (200 − x) 2 1 25 = 4(200 − x) 2 16(1502 + (200 − x) 2 ) 1 25 = (200 − x) 2 4(1502 + (200 − x) 2 ) 4(150 2 + (200 − x) 2 ) = 25(200 − x) 2 300 2 + 4(200 − x) 2 = 25(200 − x) 2 21(200 − x) 2 = 300 2 (200 − x) 2 = 30000 7 30000 200 − x = ± 7 30000 x = 200 ± 7 x = 134.535, 265.465 30000 T (x) < 0 when x < 200 − 7 30000 T (x) > 0 when x > 200 − 7 There is a minimum at x = 134.535 The dog should run 134.535 feet before jumping in the water. 7
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Page 5: m ′′ (x) = 360 − 60x 2 m = 18
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Page 11 and 12: 9. 10. 11. Answer: Answer: 2x − s
Page 13 and 14: 14. Answer: ln(y) = ln( lim x→0 +
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Math 220 March 7 I. If 1200 cm2 of material is available to make a ...

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