Given the cubic function f(x) = x^3-6x^2 + 11x- 6, do the following: Plot the graph of the function. Find the critical points and determine whether each is a local minimum, local maximum, or a saddle point. Find the inflection point(s) (if any).Identify the intervals where the function is increasing and decreasing. Determine the end behavior of the graph.

How are the absolute maximum and minimum similar to and different from the local extrema?

Use the graph to identify any local maxima and local minima.

bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.

A simple curve that often makes a good model for the variable cost of a company, as a function of the sales level x, has the form y=p,x+B2x2+2x3. There is no constant term because fixed costs are not included. Complete parts (a) through (c). P1 B2 B C 0 y=5516086 x + (-03699737)+(00115405): (Do not round until the final answer. Then round to six decimal places as needed.) B3 B1 Pa (= b. Find the least-squares curve of the form above to fit the data (3,1.57), (5,2.03), (7,2.1), (9,2.8), (11,3.3), (13,3.5), (15,3.8), and (17.4.34), where x and y represent sales and costs in thousands. Produce a graph that shows the data points and the graph of the cubic approximation.

The demand function for the manufacturer of a product is p = f (q) = 200-5q, where p is the price (in dollars) per unit when q units are demanded (per week). Identify the function that maximizes the manufacturer's total revenue. Determine this income.

A sugar refinery can produce x tons of sugar per week at a weekly cost of 0.1x2 + 3x + 1690 dollars. Find the level of production for which the average cost is at a minimum and determine the average cost and marginal cost at that level of production. The level of production for which the average cost is at a minimum is x = |tons.

Find the local maximum and minimum values and saddle point(s) of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) f (x, у) %3D ху — 3х-Зу-х2 -у2 local maximum value(s) local minimum value(s) saddle point(s) (х, у, 0) %3D

The financial department for a company established the following cost function for producing and selling x thousand notebook computers: C(x) = 4,000 + 500x thousand dollars Write a profit function for producing and selling x thousand notebook computers and indicate its domain. Complete the below table, computing profits to the nearest thousand dollars. Note: Price-demand function = p(x) = 2,000 – 60x. Domain = 1 <= x <= 25. Revenue already calculated for you x (thousands) R(x) = Revenue C(x) = Costs P(x) Profit (thousand $) 1 1,940 -2,560 5 1,700 10 1,400 15 1,100 20 800 25 500

F(x)= 4x6- 7x5 find local minimum.