Here are the main points that will be addressed in the videos. Please read these and think about them as you watch.
- In addition to defining the derivative of a function at , the limit definition of derivative can be used to calculate the instantaneous rate of change of with respect to at a specific value of .
- Using the limit definition of derivative to compute instantaneous rates of change requires algebraically manipulating the difference quotient to cancel the in the denominator so that the limit can be easily evaluated.
- Multiplying the numerator and denominator of the difference quotient by the conjugate of the numerator is a potentially useful strategy for algebraically manipulating the difference quotient to compute the instantaneous rates of change of square root functions.