MATH 140 FIRST EXAM (2.1 – 3.1)

NAME:____________________________

Time: 60 minutes

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Possible points are in parentheses

1. (5 each)

a. Complete the following definition: The tangent line to the curve y = f(x) at the point P(a,f(a)) is the line through P with slope m = ...

There are 2 equivalent definitions. Give them both.

b. Using one of the definitions you gave above, find the slope of the tangent line to the curve f(x) = at the point P(1,3). Find the equation of the tangent line and put it in the form y= mx + b.

c. Now, sketch the graph. Show the vertex. Graph the tangent line on the same set of axes. Show all intercepts.

2. (5) Use the graph above to sketch the graph of the derivative function below.

3. Evaluate the following limits. Explain your reasoning: (5 each)

a.

b.

4. The displacement in meters of a particle moving in a straight line is given by the rule , t in seconds. (5 each)

A. Find the average velocity on the time interval [3,4]. What are the units of average velocity?

B. Find the instantaneous velocity when t=3. What are the units?

(You must use the limit definition; not the derivative rules.)

5. (5)

.

6. (5)