1. Applications of derivatives

2. Increasing/Decreasing The slope of a graph is positive or negative. It is found by taking the derivative of the given function. Set the derivative equal to zero and test value on either side.

3. Local Min/max To find them, first derive the original function. Then set it equal to zero. Test values on either side of the zero. Min refers to a point where the slope is zero. It goes from decreasing to increasing Max goes from increasing to decreasing

4. Absolute Min/max Highest point on an interval, endpoint and min/max’s should be checked

5. Concavity Concave up- the second derivative yields a positive number Concave down- the second derivative yields a negative number

6. Points of inflection Points where a graph changes concavity, the second derivative equals zero

7. Position/Velocity/Acceleration Velocity is the derivative of position. Acceleration is the derivative of velocity. Velocity is the integral of acceleration. Position is the derivative of Velocity

8. Optimization Optimization requires the minimum or maximum value. Therefore taking the derivative of the given function is necessary. Then set the function equal to zero and solve.

9. Related Rates The rate of change of one value in relation to another in the same function can lead you to find other variables. Ex: A’=B’H+H’B If you know any four of these variables you can find the other