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- How do I find the critical numbers for the function f(x) = x2 – 4x + 2?Suppose we have a revenue function given by R(x)=3x^3−αx, where α is a constant. What would the value of α need to be to have an average revenue of $10 when x=5?A researcher at a textbook manufacturing company finds that the revenue is given byR(x)=5x2−40x.What is the marginal revenue at x=20, and what does it mean?Select the correct answer below:The marginal revenue is $40, which means that revenue increases by $40 for each additional textbook produced.The marginal revenue is $160, which means that revenue is $1,600 when 10 textbooks are produced.The marginal revenue is $160, which means that when 20 textbooks are produced, the revenue increases by $160 for each additional textbook produced.The marginal revenue is $40, which means that revenue is shrinking at the rate of $40 per textbook produced.
- Solve the critical points of f(x)=2x²(x-3) ² for x only.In a certain company, the income from the sale of x thousand pieces of products is given by I (x) = 9x, while the cost of making the same x products is given by C (x) = x ^ 3-6x ^ 2 + 15x + 1. Assuming that I and C are in thousands of dollars and everything produced is sold, what is the maximum profit the producer can make? Argues using first or second derivative criteria.suppose that the price per unit in dollars of a cell phone production is modeled by p=$85-0.0125x, where x is inthousands of phones produced, and the revenue represented by thousands of dollars is R=x • p. find the production level that will maximize revenue. ____________ thousand phones
- Suppose that, in a monopoly situation, the equation is P (X) = 6-0.2 (4x-x ^ 2), where P (X) dollars is the price per item when X items are demanded. If C (x) = 2x + $ 100 is the total cost of producing and selling X items, find the marginal utility for when 200 items are produced and sold.Analyze the critical points of f (x) = (2x − x2)ex .suppose a company has revenue function R(x)=10x and the cost function C(x)=2x+100, where x is the number of units produced. Find the profit or loss if the company produces 10 units