1. The four places where derivatives do not exist is:
f(x) = abs(x) It is a corner.
A cusp.
A jump in a graph, like a piecewise function.
An asymptote, such as in a rational function.
2. Implicit Differentiation- The first step is to find the derivative of each part of the equation.
After finding each variable, put the equation over dx. Ex: 2y= 2*dy/dx.
Solve for dy/dx by getting all of the variables of that type on one side.
Divide to get dy/dx by itself.
3. The most important thing to remember in a related rate problem is to write the dy/dx in the right spot. If it's put in the wrong spot or not included then the whole problem is incorrect.
