QUESTION 1

Determine whether the function's vertex is a maximum point or a minimum point. ixz+xy=3 2 O The vertex is a maximum point. C The vertex is a minimum point. J Good! Find the coordinates of this point. (X. y) =( _1' _ 7 2 V ) Find the zeros, if any exist. (Enter your answers as a commaseparated list. If an answer does not exist, enter DNE.) Find the y-intercept. X Sketch the graph of the function. 10 0.qu ' . Graph Layers After you add an object to the graph you can use Graph Layers to view and edit its nrnnerge Find the average rate of change of the function between the given values of x. y = -5x - x between x = -2 and x = 6.Complete the following. f(x) = 5x2 27x + 10 (a) Use the graph of y = f(x) to find an integer solution to f(X) = 0. X = (b) Use the solution from (a) to find a factor of f(x). (c) Factor f(x). f(X) = (d) Solve f(x) = 0. (Enter your answers as a comma-separated list.) x: The owner of an apartment building can rent all 60 apartments if she charges $1,600 per month, but she rents one fewer apartment for each $50 increase in monthly rent. (a) Construct a table that gives the revenue generated if she charges $1,600, $1,650, and $1,700. No. of Apts Rent Total Revenue 60 $1,600 $ 59 $1,650 $ 58 $1,700 $ (b) Does her revenue from apartment rentals increase or decrease as she increases the rent from $1,600 to $1,700? O revenue increases 0 revenue decreases (c) Write an equation that gives the revenue R, from apartment rentals if she makes x increases of $50 in the rent. R(x) = (d) Find the rent she should charge to maximize her revenue. :5 per month Suppose the percent of the total work force that is female is given by p(t) = 0.0033[2 + 0.48t + 35 where t is the number of years past 1970. (a) Graph the function y = p(t). y Y Y 70 70[ 60 60 so 50[ 40 40 30 3o[ 20 20 10 lot . . . t . . . . t 'I . . . o 50 100 150 200 (DO 50 100 150 200 (DO 50 100 150 200 (b) From the equation, identify the maximum point on the graph of y = p(t). (Round your answers to two decimal places.) (t,y)=( X ) (c) In what year is the percent of women workers at its maximum, according to this model? :i If, in a monopoly market, the demand function for a product is p 195 0.50)( and the revenue function is R = pX, where X is the number of units sold and p is the price per unit, what price will maximize revenue? $|:l Suppose a company has fixed costs of $44,800 and variable cost per unit of 3X + 222 dollars, where X Is the total number of units produced. Suppose further that the selling prIce of Its product IS 1850 X dollars per unit. (a) Find the break-even points. (Enter your answers as a comma-separated list.) x: (b) Find the maximum revenue. (Round your answer to the nearest cent.) $:l (c) Form the profit function P(x) from the cost and revenue functions. P(x) = Find maximum profit. 35 (d) What price will maximize the prot? (Round your answer to the nearest cent.) $ The data In the table give sales revenues and costs and expenses for a mining company for various years. Sales Revenue Costs and Expenses Year (millions) (millions) 2010 $2.6265 $24105 2011 2.7014 2.4412 2012 2.893 2.6378 2013 3.3351 2.9447 2014 3.9739 3.5344 2015 4.5504 3.8171 2016 4.9379 4.2587 2017 5.1856 4.8769 2018 4.9133 4.9088 2019 5.1283 4.6771 2020 4.7589 4.9025 Assume that sales revenue for the company can be modeled by R(t) = o.o31t2 + 0.784t + 0.138 where t is the number of years past 2007. (a) Use the function to determine the year in which maximum revenue occurs. : Determine the maximum revenue the function predicts. (Round your answer to two decimal places.) $ :] million (b) Check the result from (a) against the data in the table