Exam 2: Rate of Change: the Derivative

A certain function f is decreasing and concave down. In addition, and . Which of the following are possible zeroes of f? Select all that apply.

A function f satisfies the following conditions: , , , , and for . Which of the following are possible values for ? Select all that apply.

Suppose is the height in inches of a person who is t years old. Would you expect to be

Assume that f and g are differentiable functions defined on all of the real line. If for all x and if for some , then for all x.

Estimate the value of for the function .

Consider the two functions shown below. A. B.

The noise level, N, in decibels, of a rock concert is given by , where d is the distance in meters from the concert speakers. Which of the following gives the rate of change, in decibels per meter, of noise 600 meters away from the speakers?

Given the following table, find .

Your friend Herman operates a neighborhood lemonade stand. He asks you to be his financial advisor and wants to know how much lemonade he can make with the $3.12 he happens to have on hand. The only information he can give you is that once last month he spent $2 and made 19 glasses of lemonade, and another time he spent $5 and made 83 glasses of lemonade. You decide to use this data to create an exponential cost function, , giving the cost in dollars of making q glasses of lemonade. How many full cups of lemonade can Herman make with this model?

Your friend Herman operates a neighborhood lemonade stand. He asks you to be his financial advisor and wants to know how much lemonade he can make with the $3.47 he happens to have on hand. The only information he can give you is that once last month he spent $2 and made 19 glasses of lemonade, and another time he spent $5 and made 83 glasses of lemonade. Create a linear cost function, , giving the cost in dollars of making q glasses of lemonade. How many full cups of lemonade can Herman make with this model?

Using the following table, tell whether is likely greater than 0, likely less than 0, or might be equal to 0. Type "<",">", or "=".

Find the derivative of at x = 3 algebraically.

Let be the time, in minutes, that it takes for an oven to heat up to F. What is the sign of ?

Given the following data about the function, f, use an approximation of the tangent line at x=4.5 to estimate .

A certain function f is decreasing and concave down. In addition, and . Which of the following are possible values for ? Select all that apply.

The world's only manufacturer of left-handed widgets has determined that if q left-handed widgets are manufactured and sold per year at price p, then the cost function is , and the manufacturer's revenue function is . The manufacturer also knows that the demand function for left-handed widgets is . A. Write the profit function in terms of price p. B. Sketch the profit function to determine what price yields the largest profit. What is that price?

Find the derivative of at x = 2 algebraically.

The height of an object in feet above the ground is given in the following table. If the height of the object is doubled, the average velocity over any interval

Let be the amount of lumber, in board-feet, produced from a tree of radius r (measured in inches). Which of the following gives the number of board-feet obtained from a tree of radius 8 inches?

Suppose that is the cost to heat my house, in dollars per day, when the outside temperature is Fahrenheit. If and , approximately what is the cost to heat my house when the temperature is ?