*My* summary of principal subject matter for the
second exam in Math 151, fall 2007

- Important stuff from before the first exam, primarily methods of
computing limits and derivatives, preliminary ideas about graphing
(including continuity), common functions, and mathematical
modeling. Also algebraic manipulation.
- Differentiating everything in sight:
- The other common functions (exponentials, logs, inverse trig)
- Implicit differentiation
- Related rates (also mathematical models)

- The Mean Value Theorem
- Critical point analysis (0
^{th} and 1^{st} and
2^{nd} derivative tests); finding max/min of a function in an
interval.
- Curve sketching: graph properties and algebraic properties
- First derivative and {in|de}creasing
- Second derivative and concave {up|down}
- Going from a formula to a graph
- Going from a graph to a formula
- Putting it all together (including horizontal and vertical
asymptotes)

- Mathematical modeling and extreme values: drawing a diagram,
analyzing a story, getting to a calc problem, solving it, and then
*answering the question that was asked*.
- Imagining that the tangent line is really close to the graph
- Linear approximation
- Newton's method
- L'Hôpital's Rule

**
Maintained by **`
greenfie@math.rutgers.edu` and last modified 11/15/2007.