Verify that x(t)= C1et+C2 is a solution to x"-x'=0. Find C1 and C2 so that x(t) satisfies x(0)=10 and x'(0)=100. Sketch a graph of the solution x(t) given the calculated values of C1 and C2.

Suppose that for a company manufacturing calculators, the cost, revenue, and profit equations are given by x² 20' C = 90,000+ 40x, R=200x - where the production output in 1 week is x calculators. If production is increasing at a rate of 400 calculators per week when production output is 6,000 calculators. Find the rate of increase (decrease) in cost, revenue, and profit. A) Costs are increasing at the rate of $ (Simplify your answer.) B) Revenue is (Simplify your answer.) C) Profits are (Simplify your answer.) at the rate of $ P=R-C at the rate of $ per week at this production level. per week at this production level. per week at this production level.

The management of Thermomaster Company, has estimated that the total weekly cost (in dollars) for producing x thermometers is C(x) = 8000 + 5x dollars per year. Find the average cost function C

The total cost to manufacture and sell q exactotherms is given by the cost equation C(q) = 2000+5q. The revenue equation is R(q)= 40q - 0.05q^2 dollars for the sale of q exactotherms. Assume the profit is P(q)= R(q) - C (q).   Find the number of items q to sell so that the profit function P(q) has its maximum.    Find on which interval(s) the profit function is increasing and decreasing.