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The question and answer are attached. Please explain how to get answer.
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- The leading behavior h(infinity)(x) for h(x) = (1.3x+(x^3.2)+(e^2.4x))/(1.3+3.2x+(2.4x^2)) at infinity is h(infinity)(x) =Part 1.Find the dimensions of the rectangular box having the largest volume and surface area 24 square units. List the dimensions in ascending order ( , , ) Part 2.Locate all the critical points of the function f(x,y)=10x−x2−5xy2.Solve the critical points of f(x)=2x²(x-3) ² for x only.
- for some function g(x),g'(-2)=0 and g(-2)=-8. what is the critical number? What is the critical value? What is the critical point.?When the HHI is less than 1500, the market price is a competitive one, while, when the HHI is ranging from 1500 to 2500, the market is slightly concentrated. When the value is above 2500, the market is extremely concentrated. Here, for all the 3 years the HHI is above 2500, implying that the market is highly concentrated one. Question Are your conclusions for HHI consistent with the five-firm concentration in all cases? Give two reasons to support your answer.The critical values of f ( x ) = x 2 e − x 2 are?
- a) Find all of the critical points of x2 - x - 1 b) Find all of the critical points of x3 - 3x - 2f(x)=x^3+6x^2 -3x -5. Find all local minima and maxima positions as well as their optimal values. Is the local optimum solution also global?It is observed that a certain bacteria culture has a relative growth rate of 12% per hour, but in the presence of an antibiotic the relative growth rate is reduced to 5% per hour. The initial number of bacteria in the culture is 22. Find the projected population after 24 hours for the following conditions.(a) No antibiotic is present, so the relative growth rate is 12%.(b) An antibiotic is present in the culture, so the relative growth rate is reduced to 5%.
- 4. If the secant method is used on f(x) = x^5 +x^3 +3 and if x_(n-2) = 0 and x_(n-1) = 1, what is x_n?Social animals that live in groups can spread less time scanning for predators thab solitary individuals. However, they waste time fighting with the other group members over the available food. There is some group size at which the net benefits greatest becuase the animals spend the least time of these unproductive activities, and thus can spend time on feeding, mating, etc. Assume that for a group of size x, the fraction of time spent scanning for predators is s(x) = 212x 1/x+1 and the fraction of time spent fighting with other animals over food is F (x) = 4.8x (x+1)^2 Find the size of the group for which the time wasted on scanning and fighting is smallest. Round your answer to two decimal places.The function f(x) = x^3 + bx^2 + c has a critical point at (-2, 6). Determine the value of b and c.