The graph below shows a company's profit f(x), in dollars, depending on the price of pens x, in dollars, sold by the company: Part A: What do the x-intercepts and maximum value of the graph represent? What are the intervals where the function is increasing and decreasing, and what do they represent about the sale and profit? (4 points)

Part B: What is an approximate average rate of change of the graph from x = 3 to x = 5, and what does this rate represent? (3 points)

Part C: Describe the constraints of the domain. (3 points)

(a) compute the maclaurin polynomial m2(x) for f(x) = cos x. (b) use the polynomial of part (a) to estimate cos π 12. (c) use a calculator to compute the error made using the estimate from part (b) for the value of cos π 12. remember that the error is defined to be the absolute value of the difference between the true value and the estimate.

How many credit hours will a student have to take for the two tuition costs to be equal? round the answer to the nearest tenth of an hour.

Carla was trying to decide what to do saturday evening. she has $100 available to spend for the evening. she has narrowed her choices down to these events: braves game, a concert of an artist she likes, or the georgia aquarium. admission to the braves game is $25, hot dogs cost $10, sodas cost $5. the concert costs $25 for admission, $20 for a souvernir t-shirt, and $10 for a soda. the georgia aquarium has the show of a lifetime with an all you can eat and drink that costs $100. carla does not want to take any driving chances, so in addition to the cost of the aquarium, she will also need to pay for her uber/lyft, which is $15 each way. which option should carla choose if she wants to spend the least? based on that choice, what then is carla's oppotunity cost? fully explain your answer in at least one paragraph.