Math 251

Calculus I

Examination # 2A

Fall 2001

Dr. McCullough

Name _____________________________________

Directions : Find the following derivatives.

You may not use a calculator.

Each problem on this page is worth 4 points.

1. ) 2. )

3. ) 4. )

5. ) 6. )

7. )

1. ) Using the definition of derivative find for the function .

Find the derivative of the following functions.

2. )

3. )

4. )

5. )

6. ) Find by implicit differentiation.

7. ) Use a linear approximation to estimate the given number : .

You must show all of your work for any credit.

8. ) Find the second derivative of the function : .

9. ) A man starts walking north at 4 ft/sec from a point P. Five minutes later a woman starts walking south at 5 ft/sec from a point 500 ft due east of P. At what rate are the people moving apart 15 minutes after the woman starts walking ?

10. ) Find an equation of the tangent line to the curve at the point .

11. ) A particle moves according to a law of motion , , where t is measured in seconds and s in feet. Answer the following questions : ( This problem is worth 12 points total )

Clearly label your answer for each part.

a. ) Find the velocity at time t.

b. ) When is the particle at rest ?

c. ) When is the particle moving in the positive direction ?

d. ) Find the total distance traveled during the first 8 seconds.