- Use the graph of y=f(x) to make a sign chart and then find the intervals on which f is increasing, decreasing, concave up, and concave down. Also give the x-coordinates of all points of inflection. Look at problem 4.1.7.
- Sketch a continuous curve that has the stated properties. Three parts. Look at problem 4.1.29-30.
- Classify each critical point as a relative maximum, relative minimum, neither, impossible, or not enough information given. Seven parts. Know the first and second derivative tests to answer these. Note: There is a difference between you not knowing how to do it and not enough information being given. Example: If f'(3)=0 and f"(3)=-2, then there is a relative maximum at x=3.
- The derivative of a function is given. Determine any critical points and identify them as relative minimums, relative maximums, or neither.
- The graph of a polynomial function is given. Tell where f(x)=0, f'(x)=0, and f"(x)=0. Using your knowledge from college algebra and differential calculus, write a function whose graph could be that shown.
- Determine by inspection whether each of the functions will have an absolute
minimum, absolute maximum, both, neither, or not enough information given.
Six parts. Example: If f(x)=-x
^{6}over all real numbers, then there will be an absolute maximum. - Give a complete graph of the polynomial and label the coordinates of the intercepts, stationary points, and inflection points. Check your work with a graphing utility. Look at problems 4.3.1-10.
- The graph of a rational function is given. Tell where f(x)=0, f'(x)=0, and f"(x)=0. Using your knowledge from college algebra and differential calculus, write a function whose graph could be that shown.
- Given a polynomial function in factored form, answer the following questions.
Look on pages 259-260.
- What is the right hand behavior of the graph?
- What is the left hand behavior of the graph?
- Where will the graph cross the x-axis?
- Where will the graph touch the x-axis?
- Where will the graph be tangent to the x-axis?
- Where will the graph have an inflection point on the x-axis?

- The graph of y=f'(x) is given. Identify where the original function has a relative maximum, relative minimum, and point of inflection. Make a sketch that could be the graph of the original function. Look at problem 4.2.13-16.
- Find all absolute extrema, if any, on the stated interval. Two parts. Look at problems 4.5.5-22.

- There is a take home portion worth 35 points. It is due the day of the in-class exam. Each problem on the take home is worth 5 points except for #3 (6 pts) and #4 (9 pts).

# | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | Take Home | Total |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Pts | 7 | 6 | 8 | 4 | 5 | 6 | 5 | 5 | 6 | 5 | 8 | 35 | 100 |