After / hours on a particular day on the railways of the Island of Sodor, Thomas...

         

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After / hours on a particular day on the railways of the Island of Sodor, Thomas the Tank Engine is s(t) = -0.22t +2.13t2 + 27t miles east of Knapford Station (for 0 ts 12). a) Where is Thomas (both distance and direction from the starting point at Knapford Station) after 6 hours? b) What is the velocity of Thomas after 6 hours? c) What is the acceleration of Thomas after 6 hours? d) Is Thomas speeding up or slowing down after 6 hours? How can you tell? 1) For each of the following: (i) Determine the intervals on which the following functions are increasing and decreasing. (ii) Use the first derivative test to classify each of the critical points as a relative minimum, a relative maximum, or neither one. Make sure that you read the directions on the front cover before attempting problems 1, 2, and 3 and I STRONGLY recommend that you review the lecture examples referenced in those instructions to lessen the possibility of losing points due to not showing the necessary work to support your answers. a) f(x) = x - 8x380x + 400 b) g(x) = 5xe3x+2 3) For each of the following, determine the intervals on which the following functions are concave up and concave down. a) f(x)=x-5x-108x + 216x b) g(x) = 4x x-3 8) An apricot grower finds that if she plants 28 trees per acre, each tree will yield 114 bushels of star fruit. She also estimates that for each additional tree that she plants per acre, the yield of each tree will decrease by 3 bushels. How many trees should she plant per acre to maximize her harvest and what is the maximum harvest? Suppose that a homeowner wishes to construct a beach-themed petting zoo in his backyard consisting of an enclosure of four parallel rectangular pens that are fenced on all four sides as shown: Blephant Seals Lion's Mane Jellyfish Fiddler Crabs Giant Clams Banded Sea Kraits If he has a total of 2400 feet of fencing available to use to construct the enclosure, what is the maximum TOTAL area that can be enclosed? 7) Find the absolute extreme values of f(x)= x + 4x - 36x on the interval [-4, 6]. After / hours on a particular day on the railways of the Island of Sodor, Thomas the Tank Engine is s(t) = -0.22t +2.13t2 + 27t miles east of Knapford Station (for 0 ts 12). a) Where is Thomas (both distance and direction from the starting point at Knapford Station) after 6 hours? b) What is the velocity of Thomas after 6 hours? c) What is the acceleration of Thomas after 6 hours? d) Is Thomas speeding up or slowing down after 6 hours? How can you tell? 1) For each of the following: (i) Determine the intervals on which the following functions are increasing and decreasing. (ii) Use the first derivative test to classify each of the critical points as a relative minimum, a relative maximum, or neither one. Make sure that you read the directions on the front cover before attempting problems 1, 2, and 3 and I STRONGLY recommend that you review the lecture examples referenced in those instructions to lessen the possibility of losing points due to not showing the necessary work to support your answers. a) f(x) = x - 8x380x + 400 b) g(x) = 5xe3x+2 3) For each of the following, determine the intervals on which the following functions are concave up and concave down. a) f(x)=x-5x-108x + 216x b) g(x) = 4x x-3 8) An apricot grower finds that if she plants 28 trees per acre, each tree will yield 114 bushels of star fruit. She also estimates that for each additional tree that she plants per acre, the yield of each tree will decrease by 3 bushels. How many trees should she plant per acre to maximize her harvest and what is the maximum harvest? Suppose that a homeowner wishes to construct a beach-themed petting zoo in his backyard consisting of an enclosure of four parallel rectangular pens that are fenced on all four sides as shown: Blephant Seals Lion's Mane Jellyfish Fiddler Crabs Giant Clams Banded Sea Kraits If he has a total of 2400 feet of fencing available to use to construct the enclosure, what is the maximum TOTAL area that can be enclosed? 7) Find the absolute extreme values of f(x)= x + 4x - 36x on the interval [-4, 6].