Exam 4: Section 2: Applications of Differentiation

A plane begins its takeoff at 2:00 P.M. on a 2200-mile flight. After 12.5 hours, the plane arrives at its destination. Explain why there are at least two times during the flight when the speed of the plane is 100 miles per hour.

Determine whether the Mean Value Theorem can be applied to the function on the closed interval [3,9]. If the Mean Value Theorem can be applied, find all numbers c in the open interval (3,9) such that .

The height of an object t seconds after it is dropped from a height of 550 meters is Find the average velocity of the object during the first 7 seconds.

Which of the following functions passes through the point and satisfies ?

Determine whether Rolle's Theorem can be applied to on the closed interval If Rolle's Theorem can be applied, find all values of c in the open interval such that

Determine whether Rolle's Theorem can be applied to the function on the closed interval . If Rolle's Theorem can be applied, find all numbers c in the open interval such that .

A company introduces a new product for which the number of units sold S is where t is the time in months since the product was introduced. Find the average value of during the first year.

The ordering and transportation cost C for components used in a manufacturing process is approximated by where C is measured in thousands of dollars and x is the order size in hundreds. According to Rolle's Theorem, the rate of change of the cost must be 0 for some order size in the interval Find this order size. Round your answer to three decimal places.

Find a function f that has derivative and with graph passing through the point (5,6).

Determine whether Rolle's Theorem can be applied to the function on the closed interval . If Rolle's Theorem can be applied, find all numbers c in the open interval such that

Determine whether Rolle's Theorem can be applied to the function on the closed interval If Rolle's Theorem can be applied, find all numbers c in the open interval such that

Determine whether Rolle's Theorem can be applied to on the closed interval If Rolle's Theorem can be applied, find all values of c in the open interval such that

The height of an object t seconds after it is dropped from a height of 250 meters is Find the time during the first 8 seconds of fall at which the instantaneous velocity equals the average velocity.

Determine whether the Mean Value Theorem can be applied to the function on the closed interval If the Mean Value Theorem can be applied, find all numbers c in the open interval such that .

A company introduces a new product for which the number of units sold S is where t is the time in months since the product was introduced. During what month does equal the average value of during the first year?

Determine whether Rolle's Theorem can be applied to the function on the closed interval [-1,3]. If Rolle's Theorem can be applied, find all values of c in the open interval (-1,3) such that

Determine whether the Mean Value Theorem can be applied to the function on the closed interval [0,16]. If the Mean Value Theorem can be applied, find all numbers c in the open interval (0,16) such that .