Whether we are interested in a function as a purely mathematical object or in connection with some application to the real world, it is often useful to know what the graph of the function looks like. We can obtain a good picture of the graph using certain crucial information provided by derivatives of the function and certain limits.

1. Maxima and Minima

2. The first derivative test

3. The second derivative test

4. Concavity and inflection points

5. Asymptotes and Other Things to Look For