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 changes sign from positive to negative at .What can be concluded about the graph of B at the point ? ​

Consider a function .Suppose .What can be said about the function f? ​

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.Make a graph of B versus t from the time the balloon springs a leak until it is fully re-inflated.

You have the opportunity to earn some extra income by working at $28 per hour.If your marginal tax rate is 32%, how much of the hourly income will you take home after taxes? Round your answer to two decimal places, if necessary. ​

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

You are driving with your cruise control set when you encounter a slowly moving truck.You speed up to pass the truck.When you have overtaken the truck, you slow down and resume your previous speed.The graph of velocity, , is shown.Make a graph of , the acceleration.Be sure to label your graph appropriately. ​

The marginal tax rate is the additional tax owed on each additional dollar of income.

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

You are driving with your cruise control set when you encounter a slowly moving truck.You speed up to pass the truck.When you have overtaken the truck, you slow down and resume your previous speed.If represents your velocity at time t, make a graph of .Be sure to label your graph appropriately.

If is positive then the function is certain to be positive.

Consider a function .When f is decreasing, what can be said about ? ​

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

At a maximum value of , is negative.

Consider a function .When f is not changing, what can be said about ? ​

The acceleration due to gravity near the surface of Earth has a constant value of 32 feet per second per second.Explain what this fact tells us about the downward velocity of a falling object near the surface of Earth.

At a minimum value of , is 0.

Let denote sales when a dollars are spent on advertising.We find that s has reached its maximum value.What is the value of ? ​​​

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.If the current rate of production is 180 tires, what effect on profit will an increase in production have? ​ ​​

Consider a function .When is increasing, what can be said about ? ​

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