Exam 4: Applications of the Derivative

Find the horizontal and vertical asymptotes of the graph.

You are given the graph of a function f.Determine the intervals where f is increasing, constant, or decreasing.

Using the curve-sketching guide, select the graph of the function.

Find the relative maxima and relative minima, if any, of the function.

A division of Chapman Corporation manufactures a pager.The weekly fixed cost for the division is $20,000, and the variable cost for producing x pagers/week is dollars.The company realizes a revenue of dollars from the sale of x pagers/week. Find the level of production that will yield a maximum profit for the manufacturer.(Hint: Use the quadratic formula.) __________ pagers/week

Find the horizontal and vertical asymptotes of the graph. Horizontal asymptote is __________ Vertical asymptote is __________

The estimated monthly profit (in dollars) realizable by Cannon Precision Instruments for manufacturing and selling x units of its model M1 camera is To maximize its profits, how many cameras should Cannon produce each month?

A book designer has decided that the pages of a book should have margins at the top and bottom and margins on the sides.She further stipulated that each page should have an area of (see the figure). Determine the page dimensions that will result in the maximum printed area on the page.

Find the absolute maximum value and the absolute minimum value, if any, of the given function.

The graph of the function f shown in the accompanying figure gives the elevation of that part of the Boston Marathon course that includes the notorious Heartbreak Hill.Determine the intervals (stretches of the course) where the function f is increasing (the runner is laboring), where it is constant (the runner is taking a breather), and where it is decreasing (the runner is coasting).

Find the inflection points, if any, of the function.Otherwise, answer no solution.

A manufacturer of tennis rackets finds that the total cost C(x) (in dollars) of manufacturing x rackets/day is given by Each racket can be sold at a price of p dollars, where p is related to x by the demand equation If all rackets that are manufactured can be sold, find the daily level of production that will yield a maximum profit for the manufacturer.

A truck gets mpg when driven at a constant speed of x mph (between 40 and 80 mph).If the price of fuel is $1/gallon and the driver is paid $8/hour, at what speed between 40 and 80 mph is it most economical to drive?

A stone is thrown straight up from the roof of a 50-ft building.The height (in feet) of the stone at any time t (in seconds), measured from the ground, is given by What is the maximum height the stone reaches?

The number of major crimes committed in the city of Bronxville between 1997 and 2004 is approximated by the function where N(t) denotes the number of crimes committed in year t ( corresponds to 1997).Enraged by the dramatic increase in the crime rate, the citizens of Bronxville with the help of the local police organized "Neighborhood Crime Watch" groups in early 2001 to combat this menace. When was the growth in the crime rate maximal?

Determine the relative maxima and relative minima, if any.Otherwise, answer none. Relative maxima: __________ Relative minima: __________

The height (in feet) attained by a rocket t sec into flight is given by the function . When is the rocket rising and when is it descending?

Find the relative maxima and relative minima, if any, of the function.Otherwise, answer none. Relative minima: __________ Relative maxima: __________

Find the horizontal and vertical asymptotes of the graph of the function.

Show that the function is concave upward wherever it is defined.