Let f(r) = ln(r). State the domain of the function.
Find the first derivative.
Find the critical values of the function.
Use the first derivative to find all intervals of increase and decrease.
Identify any maximum and minimum points.
Find the second derivative.
Use the second derivative to find all intervals of concavity.
Identify any points of inflection.
If C(x) is the cost of producing units of a commodity, then the average cost per unit is C(r) = 6%.
Consider the cost function C(x) given by C(x) = 54,000 + 130x - 4x^2/2. (Round your answer to the nearest cent)
(a) Find the total cost at a production level of 1,000 units.
(b) Write the average cost equation and find the average cost at a production level of 1,000 units.
(c) Write an equation for the marginal cost C'(x) (the derivative of the cost C(x)) and find the marginal cost at a production level of 1,000 units.
(d) Find the production level that will minimize the average cost.
(2) What is the minimum average cost?