Nice job overall, including thoughts on sign and steepness of slope, alignment of zeros, and symmetry (about x=1, rather than about the y-axis); did use the word "horizontal asymptote", when in fact it is simply a horizontal tangent line.
Other things people considered: concavity, symmetry of g not reflected in the other functions, class of functions (although I don't recognize these, you might!).
Nice layout of the given information, nice diagram, has the right units, gives the exact answer as well as an approximation - good job!
Student missed the endpoints for the domain - still, about the only paper to get this right, demonstrating that many of you are still having trouble solving an inequality like x sin(x) >= 0.
On part 4, the student missed the fact that the derivative has a denominator, which imposes a risk of being 0. We have to eliminate those value of the domain for which x sin(x) = 0.
The student filled in the table well, noting how the chain rule was used to fill in (with an example calculation - good idea to show me that!). The graph was a problem, which almost all of you had: it seems like the graph should be linear, but the derivative denies that! You have to listen to the derivative! (I added in the little slope lines for the student, and the m=1.)
Here's a (possible) corrected graph for part 2 above: note that the derivative information from the table shows up in the slopes of the function:
Watch that you don't violate that vertical line test!
This student (and several others) actually did some mathematical modeling! Hooray! You dug into your mathematical database, and actually figured out the function. I have some confidence that this student, given data from the working world, may be able to do the same thing at work as a stock broker, or forensic scientist, or teacher, or....
Alternatively, you could make a few slope calculations, and trace in the derivative; then do the same, using the derivative curve, for the second derivative.
Because the second derivative is a constant above, the third derivative is zero, so, as our student here notes, "the jerk is 0 at any time." I especially liked the student's use of units!
F, F, F, F, T
We're using the linearization (or tangent line) about x=0 (so a=0!). Make sure that your linearization is a linear function! It should be expressible as y=mx+b (x should not appear in any denominator, for example).
Ironically, this student skipped this one!
The axes correspond to xy=0. This is actually from your book: Example 4 and Figure 7, p. 189.
The product rule was demonstrated in class, and actually appeared on the Spring exam. I was surprised at the number of students who tried to demonstrate it without being able to state it correctly! There were also too many students who could not write the definition of the derivative (often forgetting the limit). Yikes!
The derivation of the derivative of sine is also in your book. Proving it from the definition involves knowing some of the special limits (see p. 171).