Exam 2: Rate of Change: the Derivative

Give the difference quotient approximation to 2 decimal places of where .

Using the graph of , at x=D is positive, negative or zero?

Cost and revenue functions for a certain chemical manufacturer are given in the following figure. When does Revenue=Cost?

Assume that f and g are differentiable functions defined on all of the real line. If everywhere and everywhere then .

Cost and revenue functions for a certain chemical manufacturer are given in the following figure. What is the current sale price?

Let be the temperature in degrees Celsius at a height h (in meters) above the surface of the earth. Which of the following gives the height, in meters, at which the rate of change of temperature with respect to height is 25 degrees per meter?

Let . Write an equation for the line tangent to the graph of at the point where x = 4.

Let be the fuel efficiency of a car moving at v miles per hour. with efficiency measured in miles per gallon. Suppose and . What would you expect to be?

If is the length of the side of a cube in terms of its volume, then calculate the average rate of change of x with respect to V over the interval 1<V<2. Round to 2 decimal places.

The first figure shows the graph of the derivative of a function. Could the second figure be the original function?

Find algebraically by using the limit definition if .

Could the function on the right be the second derivative of the function on the left?

A table of values is given for . A. Is positive or negative? B. Is positive or negative? C. Approximate by averaging the approximations from either side.

Considering the graphs below, could f(x) be the derivative of g(x)?

The population of a certain town is given by the function where t is the number of years since the town was incorporated. If is constant for t >185, what will be if and ?

The cost of mining a ton of coal is rising faster every year. Suppose is the cost of mining a ton of coal at time t. Which of the following must be positive? Select all that apply.

The cost of extracting T tons of ore from a copper mine is dollars. What are the units for ?

Let represent the dollar amount charged per hour by a computer consultant to a client when they sign a contract t hours of work. The consultant gives a discount to the client if the contract is increased by 10 hours. Estimate the amount charged per hour when the client orders 130 hours of work.

The height of an object in feet above the ground is given in the following table. The average velocity over the interval is _____ feet/sec.

A newspaper headline recently read , " Taxes are increasing at an decreasing rate". This says that the second derivative is negative.