Final Exam Problems

(Please extend sufficient space if you work on the docx version)

[10 points]

Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function:

[20 points]

Let , where is the function whose graph is shown below.

Evaluate , , , , and

On what intervals is increasing?

Where does have a maximum value?

Sketch a graph of the function

[25 points]

Use Part 2 of the Fundamental Theorem of Calculus to evaluate the definite integral.

[10 points]

Find the indefinite integral:

[10 points]

Find the area of the region bounded by the curves: and

[10 points]

Find the average value of the function on the interval

[9 points]

A tennis ball is thrown vertically downward from a height of 54 feet with an initial velocity of 8 feet/sec.

What is the velocity of the ball at time ?

What is the position of the ball at time ?

What is the impact velocity if it hits a 6-foot tall person on the head?

[6 points]

The fuel tank on a large truck has trapezoidal cross sections with dimensions (in feet) shown in the figure below. Assume that the engine is approximately 2 feet above the top of the fuel tank and that diesel fuel weighs approximately 55.6 pounds per cubic foot.

Find the work done by the fuel pump in raising a full tank of fuel to the level of the engine.

Hint: Use the fact that