Complete solutions are required. Otherwise stated, calculators are NOT allowed. You may leave your answer in a calculator-ready format. 1 1. /2+4+4=10 marks/ Consider a function f (x) = 1 - In(1540) which has the derivatives In (154x) + 1 f'(x) = x(1 - In (154x))? and f"(x) = - x2 (In (154x) - 1) (a) /2 mark Find the domain. State it using interval notation. (b) /4 marks) Find the intervals on which f(@) is increasing or decreasing and classify the local extreme values (if they exist) (c) /4 marks) Determine f(@) is concave up or down and find the inflection points. 3. /3+2-5 points/ Answer the following questions: (a) /3 points) Find a cubic function f (a cubic function is a polynomial of degree 3) that has the inflection point (0, 0) and the critical number 1 with f(1) = 2024. Hint: What does this information tell you about the values of the function and its derivatives at a = 0 and x = 1? (b) /2 points) Does the function f from part (a) have inflection points or critical numbers in addition to those given in part (a)?4. /2+4+4=10 points Rogers Place can hold a maximum number of 18,500 fans for an Edmonton Oilers hockey game. Based on historical data, at an average ticket price of $200, an average of 16,000 fans buy a ticket and attend the game. For each $5 that the average ticket price is increased (or lowered), 500 fans less (or more) buy a ticket. (a) /2 points) Let a(p) be the number of fans attending a game at an average price p. Determine the function a (p) assuming it is linear. (b) /4 points) What is the average ticket price at which the revenues are maximized? (c) /4 points) Because of hype around the team, the demand for tickets to Oilers hockey games has risen. At an average ticket price of $200, an average of 18,000 fans buy a ticket and attend the game this season. Still for each $5 the average ticket price is increased (or lowered), 500 fans less (or more) buy a ticket. Using this information, what is now the average ticket price at which the revenues are maximized