Exam 4: Applications of the Derivative

A rectangular box is to have a square base and a volume of 4 ft.³. If the material for the base costs 20 cent/square foot, the material for the sides costs 30 cent/square foot, and the material for the top costs 10 cent/square foot, determine the dimensions of the box that can be constructed at minimum cost. ​ ​

The average cost per disc (in dollars) incurred by Herald Records in pressing x DVDs is given by the average cost function ​ ​ Find the horizontal asymptote of . ​ __________ ​ What is the limiting value of the average cost? ​ __________

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

The quantity demanded each month of the Sicard wristwatch is related to the unit price by the equation , where is measured in dollars and is measured in units of a thousand. ​To yield a maximum revenue, how many watches must be sold? ​

Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. If is increasing on , then for each in .

If an open box has a square base and a volume of 864 in.³ and is constructed from a tin sheet, find the dimensions of the box, assuming a minimum amount of material is used in its construction. ​

Find the relative maxima and relative minima of the function. ​ ​

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

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

Use the information summarized in the table to select the graph of Domain: Intercept: y-intercept: 03 Asymptotes: None Intervals where f​ is ↑ and ↓: ↑ on ↓ on Relative extrema: Rel. min. at ; rel. ma. at Concavity: Downward on ; upward on Point of inflection: ​

A truck gets 600/x 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? ​

Find the inflection points, if any, of the function. ​ ​

Select the graph of the function using the curve-sketching guide. ​ ​

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

A stone is thrown straight up from the roof of a 90-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? ​

Find the inflection points, if any, of the function. ​ ​

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

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

One of the functions below is the derivative function of the other. Identify each of them. ​ ​

An apple orchard has an average yield of 30 bushels of apples/tree if tree density is 25 trees/acre. For each unit increase in tree density, the yield decreases by 2 bushels. How many trees should be planted in order to maximize the yield? ​