9 4 (1 point) Consider the function f(x)= x3 x5 Let F(x) be the antiderivative of...

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9 4 (1 point) Consider the function f(x)= x3 x5 Let F(x) be the antiderivative of f(x) with F(1) = 0. Then F(x) = - 9 4 1 + + + 9 x4 ZI (1 point) The manager of a large apartment complex knows from experience that 120 units will be occupied if the rent is 324 dollars per month. A market survey suggests that, on the average, one additional unit will remain vacant for each 1 dollar increase in rent. Similarly, one additional unit will be occupied for each 1 dollar decrease in rent. What rent should the manager charge to maximize revenue? (1 point) A small island is 4 miles from the nearest point P on the straight shoreline of a large lake. If a woman on the island can row a boat 2 miles per hour and can walk 3 miles per hour, where should the boat be landed in order to arrive at a town 6 miles down the shore from P in the least time? Let x be the distance between point P and where the boat lands on the lakeshore. Hint: time is distance divided by speed. (A) Enter a function 7(x) that describes the total amount of time the trip takes as a function of the distance x. T(x)= (B) What is the distance x = c that minimizes the travel time? Note: The answer to this problem requires that you enter the correct units. C= (C) What is the least travel time? Note: The answer to this problem requires that you enter the correct units. The least travel time is (D) Recall that the second derivative test says that if T'(c) = 0 and T" (c) > 0, then 7 has a local minimum at c. What is T" (c)? T" (c) = 9 4 (1 point) Consider the function f(x)= x3 x5 Let F(x) be the antiderivative of f(x) with F(1) = 0. Then F(x) = - 9 4 1 + + + 9 x4 ZI (1 point) The manager of a large apartment complex knows from experience that 120 units will be occupied if the rent is 324 dollars per month. A market survey suggests that, on the average, one additional unit will remain vacant for each 1 dollar increase in rent. Similarly, one additional unit will be occupied for each 1 dollar decrease in rent. What rent should the manager charge to maximize revenue? (1 point) A small island is 4 miles from the nearest point P on the straight shoreline of a large lake. If a woman on the island can row a boat 2 miles per hour and can walk 3 miles per hour, where should the boat be landed in order to arrive at a town 6 miles down the shore from P in the least time? Let x be the distance between point P and where the boat lands on the lakeshore. Hint: time is distance divided by speed. (A) Enter a function 7(x) that describes the total amount of time the trip takes as a function of the distance x. T(x)= (B) What is the distance x = c that minimizes the travel time? Note: The answer to this problem requires that you enter the correct units. C= (C) What is the least travel time? Note: The answer to this problem requires that you enter the correct units. The least travel time is (D) Recall that the second derivative test says that if T'(c) = 0 and T" (c) > 0, then 7 has a local minimum at c. What is T" (c)? T" (c) =

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The images you have provided contain three different math problems Lets address each of them one by one 1 Antiderivative of a function Consider the fu... View the full answer