Exam 4: Using the Derivative

For which interval(s) is the function decreasing?

The point x=1 on the following closed graph corresponds to

In the function y = 3sin (x) + 5, in the interval from 0 , at which value(s) of x does the function contain a global maximum?

The graph of the function is: A. increasing and concave up on what interval? B. increasing and concave down on what interval? C. decreasing and concave upon what interval? D. decreasing and concave down on what interval?

Given the cost function and the demand function , find the value of q (to the nearest whole number) for which average cost is a minimum.

A flu epidemic spreads amongst a group of people according to the formula , where represents the number of people that are infected by the end of day t. A. How many people are infected by the end of the fifth day (to the nearest person)? B. At what rate do the people become infected on day 5 (to the nearest person per day)?

The demand curve for a product is given by . A. Write revenue as a function of price and take its derivative to find the price (to the nearest cent) that will maximize revenue. B. Find the elasticity (to two decimal places) at the price you found in part A.

A biologist found that the number of Drosophila fruit flies, N(t), assumes the following growth pattern if the food source is limited: . A. How many fruit flies were there in the beginning (to the nearest fly)? B. At what time was the population increasing most rapidly (to the nearest day)? C. At what rate does the number of fruit flies increase after 5 days (to the nearest fly per day)?

Daily production levels in a plant can be modeled by the function , which gives units produced at t, the number of hours since the factory opened at 8 am. Factory productivity is at a maximum at _____ am.

In Wilson corners, population 2000, a rumor spreads according to the logistic model. If 5 people know the rumor at 4 PM and 110 people have heard it by 5 PM, how many people will have heard the rumor by 6 PM (to the nearest person)?

Given the following table of production quantities with their corresponding marginal revenue and marginal cost, estimate the production level that maximizes profit.

For , determine the horizontal intercept.

A normal distribution in statistics is modeled by the function . Determine where the maximum value of the function would occur.

A disease is released into a town. The number of people, in thousands infected is modeled by the equation . How many people are infected after hours?

The dose response curve in the following figure is given by , where R is percent of maximum response and x is the dose of the drug in mg. The inflection point is at (10,50) and . Would be greater or less than 7 for values of x less than 10?

Which average cost function corresponds to the total cost function shown in the following figure?

The revenue for selling q items is and the total cost is . A. Write a function that gives total profit earned. B. Find the quantity that maximizes profit.

The quantity of a medication in the bloodstream t hours after it is ingested is given, in mg, by . What is the maximum quantity of the medication in the bloodstream?

Consider the following graph of a function. Assume the entire graph is shown. How many local minima does the function have?

The total cost, C, in dollars,when producing q items is . Calculate and interpret the marginal cost if q= 6.