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

1. 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.
2. Differentiating everything in sight:
1. The other common functions (exponentials, logs, inverse trig)
2. Implicit differentiation
3. Related rates (also mathematical models)
3. The Mean Value Theorem
4. Critical point analysis (0th and 1st and 2nd derivative tests); finding max/min of a function in an interval.
5. Curve sketching: graph properties and algebraic properties
1. First derivative and {in|de}creasing
2. Second derivative and concave {up|down}
3. Going from a formula to a graph
4. Going from a graph to a formula
5. Putting it all together (including horizontal and vertical asymptotes)
6. 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.
7. Imagining that the tangent line is really close to the graph
1. Linear approximation
2. Newton's method
3. L'Hôpital's Rule