Exam 10: Derivatives

A product can be produced at a total cost dollars, where x is the number produced. If the total revenue is given by dollars, find the maximum profit. Round your answer to the nearest dollar. ​​

The following figure shows the growth of a population as a function of time. Which of A, B, and/or C correspond(s) to the upper limit of population?

A function and its first and second derivatives are given. Use these to find any relative maxima.

A function and its first and second derivatives are given. Use these to find any points of inflection. Round your answers to two decimal places. ​

Analytically determine any relative maxima. Round your answer to two decimal places.

The consumer price data can be modeled by the function , where represents 1945 and c(x) is the consumer price index (CPI) in year . During what year does the model predict that the rate of change of the CPI reached its maximum? ​​

The profit function for a commodity is dollars. Find the maximum profit. Round your answer to the nearest dollar. ​​

A company handles an apartment building with 80 units. Experience has shown that if the rent for each of the units is $360 per month, all the units will be filled, but 1 unit will become vacant for each $10 increase in the monthly rate. What rent should be charged to maximize the total revenue from the building if the upper limit on the rent is $600 per month? ​

A function and its graph are given. Use the graph to find , if it exists, where . Confirm your results analytically. ​ ​

If the total revenue function for a blender is , determine how many units x must be sold to provide the maximum total revenue in dollars. ​​

A function and its graph are given. Use the graph to find the horizontal asymptotes, if they exist, where . Confirm your results analytically. ​ ​ ​

Use the graph of to identify at which of the indicated points the derivative does not change sign. ​ ​

Find any horizontal asymptotes for the given function.

For the given function, find the critical values.

For the given function, find intervals of x-values where the function is decreasing.

For the given function and graph, estimate the coordinates of the relative minima by observing the graph, where . ​ ​

Use the graph of to identify at which of the indicated points the derivative changes from negative to positive. ​

The millions of worldwide cellular subscribers can be modeled by where t is the number of years past 1994. In what year does the model predict the number of worldwide cellular subscribers will reach a maximum? ​

Both a function and its derivative are given. Use them to find intervals on which the function is decreasing.

A kennel of 750 square feet is to be constructed as shown. The cost is $9 per running foot for the sides and $3 per running foot for the ends and dividers. What are the dimensions of the kennel that will minimize the cost? ​ ​