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.
Aren't related rates only the ones over dt?
ReplyDeleteYes you are correct. And most often word problems I believe.
DeleteNice picture. Related rates usually involve time since that is the most limiting factor for most real world problems.
ReplyDelete