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Find the interval or invtervals where the function is increasing and decreasing
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- Does the equation y=2.294e0.654t representcontinuous growth, continuous decay, or neither?Explain.This week a factory is producing 50 units of a particular commodity, and the amount being produced is increasing at the rate of 2 units per week. If C(x) dollars is the total cost of producing x units and C(x) = 0.08x3 − x2 + 10x + 4 , find the current rate at which the production cost is increasing.If 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?
- A firms production function is π = 4x+8y-3x2-2xy-3y2 and it maximum output capacity 2x+y=15 What would be the estimation of the effect on profit if output capacity is expanded by 1 unit? A) Profit will increase approximately by 8 B) Profit will decrease approximately by 16 C) Profit will decrease approximately by 16 D) Profit will increase approximately by 16Find the general solution of dy/dx=x-4/x^2-5x+6Consider the following real-world problem: Suppose that the population of Memphis is 22,400, and 60% of the population are susceptible to contract a serious illness from a very contagious bacteria that was introduced as a form of biological warfare. The remaining people have no reaction to the bacteria. Assume the susceptible people are equally mixed throughout the population. On January 1, 2022 (time t=0), the number N(t) of people who had contracted the disease was 180 and was increasing at the rate of 39 per day. Assume that N’(t) is proportional to the product of the numbers of those who have caught the disease and of those who have not. Write the differential equation that models the physical situation and solve for the exact answer.