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# Applications of derivatives

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### Applications of derivatives

1. 1. Applications of derivatives<br />
2. 2. Increasing/Decreasing<br />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.<br />
3. 3. Local Min/max<br />To find them, first derive the original function. Then set it equal to zero. Test values on either side of the zero.<br />Min refers to a point where the slope is zero. It goes from decreasing to increasing<br />Max goes from increasing to decreasing<br />
4. 4. Absolute Min/max<br />Highest point on an interval, endpoint and min/max’s should be checked<br />
5. 5. Concavity<br />Concave up- the second derivative yields a positive number<br />Concave down- the second derivative yields a negative number<br />
6. 6. Points of inflection<br />Points where a graph changes concavity, the second derivative equals zero<br />
7. 7. Position/Velocity/Acceleration<br />Velocity is the derivative of position. Acceleration is the derivative of velocity. <br />Velocity is the integral of acceleration. Position is the derivative of Velocity<br />
8. 8. Optimization<br />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.<br />
9. 9. Related Rates<br />The rate of change of one value in relation to another in the same function can lead you to find other variables.<br />Ex: A’=B’H+H’B<br />If you know any four of these variables you can find the other<br />