Exam 28: Rates of Change for Other Functions

Let B denote the price of a bag of groceries at time t.It is found that is positive at .What can be concluded about the graph of B at the point ? ​​

The CEO of a tire company has kept records for the profit P when n tires are produced.The rate of change is the marginal profit.The graph of marginal profit is shown.According to the graph, how many tires per day should the company be producing in order to maximize profit? ​ ​

You are driving and press on the accelerator to increase your velocity.What can be said regarding your acceleration? ​

You are driving with your cruise control set.What can be said regarding your acceleration? ​

A balloon is initially full of air, but then it springs a leak.Air leaks at a constant rate from the balloon.After a while the leak is patched and a pump is attached to the balloon.It is re-inflated to its original volume: Air is pumped at a constant rate that is larger than the rate of the leak.Let B denote the volume, in cubic inches, of air in the balloon after t minutes.The graph of B versus t from the time the balloon springs a leak until it is fully re-inflated is shown.Make the graph of . ​

Consider a function .If the graph of is below the horizontal axis, what can be said about the graph of f? ​

Consider a function .If the graph of f is increasing, what can be said about the graph of ? ​

Let denote sales when a dollars are spent on advertising.If is positive, what will be the effect on sales if advertising is increased? ​​

The rate of change in velocity is acceleration.

You are considering buying three stocks, Stock 1, Stock 2, and Stock 3, and their prices at time t are given by , , and , respectively.You observe that is positive, is near 0, and is negative.Which stock is likely to provide the best growth in the short term? ​​

If denotes the profit earned from an investment of I dollars, then represents the marginal profit.

Consider a function .If the graph of is constant, neither increasing nor decreasing, what can be said about the graph of f? ​

Consider a function .If the graph of f is constant, neither increasing nor decreasing, what can be said about the graph of ? ​

Let B denote the price of a bag of groceries at time t.It is found that is negative at .What can be concluded about the graph of B at the point ?​ ​​

Consider a function .If the graph of f is decreasing, what can be said about the graph of ? ​

If is negative then the function is decreasing.

If denotes the tax owed on an income of I dollars, then represents the marginal tax rate.

Consider a function .If is constant and negative, what can be said about the function f? ​

The marginal profit is the additional profit earned on each additional dollar of investment.

Consider a function .If is constant and positive, what can be said about the function f? ​