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A:
Find the inverse of the function.
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- 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.Find the positive critical point of the function f(x)=x/x^(8)+6Then 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=2
- Analyze the critical points of f (x) = (2x − x2)ex .The growth of bacteria in food products makes it necessary to time-date some products (such as milk) so that they will be sold and consumed before the bacteria count is too high. Suppose for a certain product that the number of bacteria present is given byƒ(t) = 500e0.1t,under certain storage conditions, where t is time in days after packing of the product and the value of ƒ(t) is in millions. (a) If the product cannot be safely eaten after the bacteria count reaches 3000 million, how long will this take?(b) If t = 0 corresponds to January 1, what date should be placed on the product?Consider the production function: Y = 0.75X + 0.0042X2 – 0.000023X3 At what level of X, the output will be maximum?
- Find the critical points of the function f(x)=2x^2−4x.Suppose the Marginal product of labor in the economy is given by MPN= .002(16,000-N), while the supply of labor is N=1000 + 1000w. Find the market clearing real wage rate and level of employment. What happens to the wage rate and employment if wealth rises, reducing the supply of labor to N= 500 + 1000w? As in (a), what is the unemployment rate if real wage is 1 more than the equilibrium wage? (hint: solve the real wage and then add it by 1, then find the difference of quantity of labor supplied and demanded).What are the critical points and inflection points of the equation 1/(x(x+1)^2)