Curve Sketching

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.

Maxima and Minima

The first derivative test

The second derivative test

Concavity and inflection points

Asymptotes and Other Things to Look For