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? (2 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? (2 points)Part C: Describe the constraints of the domain. (2 points)

A firm’s price in a perfectly competitive market is 1000. Its cost function is 32 C(x) = 0.01x 3x− 11+08x 96+0 , where x ≥ 0 is the number of units produced and sold. (a) Find an expression for the profit function π(x) for x ≥ 0. (b) Find all stationary points and determine the profit maximising level of output. answer to six decimal places. 1 √1−𝑥𝑥 . State your answer using (c) Using a sign diagram, determine the intervals over which π(x) is increasing and decreasing. (d) Determine the intervals over which π(x) is concave and convex. (e) Where is the point of inflection in C(x)? Give an economic interpretation of the point of inflection.

The manager of a furniture factory finds that it costs $2400 to manufacture 100 chairs in one day and $4800 to produce 300 chairs in one day.(a) Express the cost C (in dollars) as a function of the number of chairs x produced, assuming that it is linear.C = 0.25d+390 Sketch the graph. (b) What is the slope of the graph?What does it represent?It represents the time (in days) to produce each additional chair.It represents the number of chairs produced.    It represents the cost (in dollars) of operating the factory daily.It represents the cost (in dollars) of producing each additional chair.(c) What is the y-intercept of the graph?What does it represent?It represents the time (in days) to produce each additional chair.It represents the number of chairs produced.    It represents the cost (in dollars) of producing each additional chair.It represents the fixed daily cost (in dollars) of operating the factory. Viewing Saved Work Revert to Last Response17.[–/6 Points]DETAILSSESSCALC2 1.2.014.MY NOTESASK YOUR TEACHERPRACTICE ANOTHERThe monthly cost of driving a car depends on the number of miles driven. Lynn found that in May it cost her $505 to drive 460 mi and in June it cost her $565 to drive 700 mi.(a) Express the monthly cost C as a function of the distance driven d, assuming that a linear relationship gives a suitable model.C(d) = (b) Use part (a) to predict the cost of driving 1100 miles per month.$ (c) Draw the graph of the linear function. What does the slope represent?It represents the fixed cost (amount she pays even if she does not drive).It represents the cost (in dollars) of driving.    It represents the cost (in dollars) per mile.It represents the distance (in miles) traveled.(d) What does the y-intercept represent?It represents the fixed cost (amount she pays even if she does not drive).It represents the distance (in miles) traveled.    It represents the cost (in dollars) of driving.It represents the cost (in dollars) per mile.(e) Why does a linear function give a suitable model in this situation?A linear function is suitable because the monthly cost increases as the number of miles driven decreases.A linear function is suitable because the monthly cost increases even if the miles driven is constant.    A linear function is suitable because the monthly cost is fixed despite the fact that the miles driven may vary.A linear function is suitable because the monthly cost increases as the number of miles driven

The revenue and cost functions, both in dollars, for the production and sale of x TVs are given as R(x) = 160x − 0.8x2 and C(x) = 3,240 + 15x, respectively.(a)Find the value(s) of x where the graph of R(x) has a horizontal tangent line with correct units. (Enter your answers as a comma-separated list. Round your answers to the nearest integer. If an answer does not exist, enter DNE.)x = 100   (b)Find the profit function in terms of x. (Note: Profit is revenue minus costs.)P(x) = −.8x2+145x−3240 (c)Find the value(s) of x where the graph of P(x) has a horizontal tangent line with correct units. (Enter your answers as a comma-separated list. Round your answers to the nearest integer. If an answer does not exist, enter DNE.)x = 7258​

Find the breakeven point for the firms with total revenue R(x)=〖-4x〗^2+72x and a cost function of C(x)=16x+180. Sketch the graph to show the breakeven points for the the firms.

Suppose a job pays $20$20 per hour. A graph of income based on hours worked is shown below. Use the graph to determine how many hours are required to earn $60$60. SolutionAgain, we can tell right away that we have a linear function. This function represents the relationship between time and money.Let’s go through our checklist of what we should look at when given graphs.What are the labels, scale, and units on the graph? What does that tell me about the situation? (View answer)What pattern do I see? Is it consistent/does it stay the same? What does that tell me about the slope? (View answer)The slope for this graph is $$ per hour.Where does the graph begin? Is it continuous? Where does it cross the y𝑦-axis (y𝑦-intercept) and what does that mean? (View answer)Therefore, the y𝑦-intercept for this graph is (( ,, )).What are my domain and range in this context? Are there any values that wouldn’t make sense? (View answer)By finding the amount of $60$60 on the vertical axis, you can follow a horizontal line through the value, until it meets the graph. Follow a vertical line straight down from there, until it meets the horizontal axis. There, the value in hours is . This means that the number of hours of work needed to earn $60 is hours.CheckQuestion 1