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- bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.A company produces chocolate Easter bunnies at a cost per unit of 0.60 + 0.005x dollars, where x is the number produced. If the price on the competitive market for a bunny this size is $5.00, how many should the company produce to maximize its profit?Find the marginal cost function. C(x)=180+2.8x−0.05x2 C′(x)=
- 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?Then what would the value of x be if g(x) is less than or equal to 0 and also how do you find the net change in g between x=1 and x=2If the total revenue function for a hammer is R = 36x-0.001x^2, then sales of how many hammers, x, will maximize the total revenue in dollars?
- f(x) from initial value problemSuppose we have a revenue function given by R(x) = 3x3 - ax, Where a is a constant. What would the value of a need to be to have an average revenue of $10 when x = 5?Suppose that a political campaign by Loki estimates that the candidate’s polling percentage yand the amount x (in hundred thousands of pesos) that is spent on television advertising arerelated by y = e^0.3x + (5lnx)^2 while the amount that is spent on social media advertising are related by (x −3)^4 + 3y = x. (a) If P300,000 has been spent on television advertising by Loki’s campaign, determine therate of spending that will increase his polling percentage by 2 percentage points per week. (b) Suppose that Loki’s political adversary, Thor, is slowly ramping up his presence on socialmedia. If Loki’s team plans on spending P400,000 on social media advertising and the rateof spending is at P100,000 per week, at what rate will the polling percentage increase?
- With data from the Social Security Trustees Report for selected years from 1950 and projected to 2030, the number of Social Security beneficiaries (in millions) can be modeled by B(t) = 0.00024t3 − 0.026t2 + 1.6t + 2.2Find the break-even point for the firm whose cost function C and revenue function R are given. C(x) = 120x + 24,000; R(x) = 300x (x,y )=