Test 3 key

This student did a nice job. He chose particular estimates for the critical values (rather than simply labelling them, as I suggested), but that's okay. He's got a great comic-book sketch of the function in the row dedicated to f:
Problem 2 slew you (and hence me), because so many of you differentiated the parameters. Parameters are fixed values with respect to x: their derivatives are constants.
This student dropped an a²b² term (which didn't affect the derivative calculation), but which did impact the branches calculation. Pretty good job otherwise. This student also knows the relationship between an ellipse and a circle, which I had thought would be a freebie, but which mystified too many students. Know the equation of an ellipse: you're flying on one (the Earth about the sun).
- If I don't forbid it, use your calculator to find or check derivatives.
- Your calculator treats unspecified letters in an equation as parameters, and hence as constants. If you want to make sure that the calculator treats your variables properly, write the variables as "y(x)" (for example).
  So in this problem, you could define the function of x on the left-hand side by
  (x-x0)^2/a^2+(y(x)-y0)^2/b^2 and then differentiate as usual.
  Note: one thing to be careful of is if you've defined parameters a, etc. already. In that case, you need to "DelVar" them (from the F4 menu).
A very nice job by this student. Only a couple of things I would change:
1. write that dr/dt is approximately 1.37 (the first answer was exactly right).
2. I believe that on part C the student got to thinking about the change in the rate of change, whereas it's constant. The student correctly wrote that dV/dt=1oz/second.
3. Ditto comment 1. on part d: the first answer was exactly right; the second, approximate.
The sign error was a killer on this effort, but the student did a great job of marching through all this. As I note on her page, this kind of error should send up a red flag, and hopefully you'd go back and find it. But in the time allotted, that might not be possible.... A couple of things:
- If I don't forbid it, use your calculator to find derivatives! It saves you time, and is more sure than you are, typically.
- Your calculator treats unspecified letters in an equation as parameters, and hence as constants. If you want to make sure that the calculator treats your variables properly (as in problem two, for example, where you could use it to find dy/dx), write the variables as "y(x)".
- You've got to know scientific notation for the numbers. It's the "EE" button on your calculator -- if you just use "e", the calculator is likely to interpret it as the number e=2.71....
An excellent job of putting it all together on this problem. I left a little space in the five requests down below, in case one needed to justify something. It would have been good to indicate exactly what the problems were at -1, etc., but fine job nonetheless.

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