Given: f(x) = (4x^2) / (3+x^2) and g(x) = (x^2-4x) / (x-3)

For Quiz 10, be able to:

1) Find the first two derivatives of both of the above functions, f(x) and g(x).

2) Find any asymptotes (horizontal, vertical, oblique) of f(x) and g(x).

3) Fill out the first derivative chart and find any mins or maxes.

4) Fill out the second derivative chart and find any inflection points.

5) Sketch both curves based on your work from (2), (3), and (4) above. In other words, you have to do more than just copy your calculator screen here...

6) Complete optimation word problems similar to those in the packet you received during class. Do NOT just glance at packet... Make sure you can complete the assigned optimization HW exercises (yellow sheet) from start to finish by practicing them.

7) Use differentials to estimate common values. We did a volume example (basically a cubic), used pi/3 to help estimate sin(1), and used 1.21 = (1.1)^2 to help estimate sqrt{1.2} during class. Therefore, on the quiz, expect a differential exercise involving something like x^4, or cos(x), or tan(x), or a cube root, or maybe 1/x...