Exam 14: Curve Sketching

Use your graphing calculator to graph f(x)= + - x.Looking at the graph,estimate the intervals where the function is concave up and concave down.Now find these intervals using the second derivative.

The cost equation for a bakery is given by C(x)= 10(x - - 120(x - 2)+ 450,where x is the number of doughnuts made (in dozens),and C(x)is the cost in dollars.Determine where the graph of the equation is concave up and where it is concave down and find any inflection points.

Find the vertical and non-vertical asymptotes of the following function.Do not sketch its graph. y =

An equation of a horizontal asymptote for the graph of y = is

The cost equation for a company is C(x)= 2 - 15 - 84x + 3100.Use the second-derivative test,if applicable,to find the relative maxima and the relative minima.

Suppose that the total number of units produced by a worker in t hours of an 8-hour shift can be modeled by the production function P(t)= 22t + 15 - .Find where the function is concave up and where the function is concave down.

Use your graphing calculator to find the absolute extrema of on (round answers to 3 decimal places).

Find the absolute extrema for y = on the interval and where they occur.

A company owns an apartment building containing 80 units.If the company charges $300 per month rent,then all units can be rented out,and for every increase of $10 per month in rent,the company will lose one customer.What rent should be charged to maximize revenue?

A real estate firm owns 70 apartments.At $200 per month each apartment can be rented.However,for each $10 per month increase,there will be two vacancies with no possibility of filling them.What rent per apartment will maximize monthly revenue?

Use your graphing calculator to graph y = - 6 + 9x- 2.Inspect the graph to estimate where the relative extrema occur.Then use the first-derivative test to find the relative extrema.

A manufacturer has to produce annually 1000 units of a product that are sold at a uniform rate during the year.The production cost for each unit is $400,and carrying costs (insurance,interest,storage,and so on)are estimated to be 5% of the value of average inventory.Set-up costs per production run are $64.Find the economic lot size.

Determine the intervals on which the function is increasing and on which it is decreasing.Also determine the points of relative maxima and relative minima. f(x)=

How many critical values does the function f(x)= 3 + 4 Have?

A new book has its monthly revenue given by R(x)= where x is the number of months after its release and R is in thousands of dollars.Find the relative extrema and use this information to determine which month will bring the greatest revenue.

Let f(x)= + - .Determine the intervals on which f is (a)Determine the intervals on which f is increasing. (b)Determine the intervals on which f is decreasing. (c)Based on your answers to parts (a)and (b),find the values of x for which f has relative maxima. (d)Based on your answers to parts (a)and (b),find the values of x for which f has relative minima.

Find the intervals where the graph of y = f(x)is concave up and where it is concave down.Do not sketch its graph.Also determine its points of inflection.f(x)= + - 3x + 7.

Sensitivity to a drug depends on the dosage size x according to the equation s = 50x - .Find the dosage that maximizes sensitivity.

A new movie has its monthly revenue given by R(x)= where x is the number of days after its release and R is in millions of dollars.Find the relative extrema and use this information to determine which day will bring the greatest revenue.

Use the second derivative test to find the relative extremas of f(x)= -4 and where they occur.If the relative extremas can not be determined by the second derivative test,state so.