M215 Project Graphing with the Derivative (Form A)

Section 4.3 - 10 points for Form A or B 5 extra credit points for the other one

Due date:

This exercise is designed to illustrate how numerical information from a function and its derivatives can be used to get a very good sense of how the function looks. While it is a good idea to use your graphing calculator to check your final answers, it would be missing the point to use it earlier. Show all calculus work!

1. Where are the zeros (roots) of the function

2. On what intervals is the function increasing?

On what intervals is it decreasing?

3. What are the local maxima and minima?

4. To save you work, the second derivative is .

Where is f concave up?

Where is f concave down?

5. Where are the inflection points?

6. Does this graph have any vertical asymptotes? If so, what are they?

If not, why not?

7. What appears to happen to f(x) when x gets very large?

What appears to happen when x gets very large and negative?

8. Using this information, sketch a graph of this function.

M215 Project Graphing with the Derivative (Form B)

Section 4.3

This exercise is designed to illustrate how numerical information from a function and its derivatives can be used to get a very good sense of how the function looks. While it is a good idea to use your graphing calculator to check your final answers, it would be missing the point to use it earlier. Show all calculus work!

1. Where are the zeros (roots) of the function

2. Does f have any points x where f ’ (x) = 0?

Does f have any points x where f ’(x) is not defined?

Hint: It might be easier to find f ’ if you distribute first, and after you get f ’ , express as a single fraction.

3. On what intervals is the function increasing?

On what intervals is it decreasing?

4. What are the local maxima and minima?

5. Does f have any points x where f ’’(x) = 0?

Where f ’’(x) is not defined?

.

6. Where is f concave up?

Where is f concave down?

7. Where are the inflection points of f ?

8. Using this information, sketch a graph of this function.