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Applications of derivatives flash cards

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Applications of derivatives flash cards

1. 1. Applications of derivatives<br />
2. 2. Increasing/Decreasing<br />
3. 3. Increasing: When the slope of the tangent line is positive.<br /> Decreasing: When the slope of the tangent line is negative.<br />
4. 4. Points of Inflection<br />
5. 5. A point when the value of the second derivative changes signs<br />
6. 6. Extreme Value Theorem<br />
7. 7. If a function is continuous on the interval [a,b] there exist numbers c and d in [a,b] such that: <br /> or<br /> f(c) ≤ f(x) ≤ f(d)<br />
8. 8. Position, Velocity, Acceleration<br />
9. 9. If you are given the position function then you can find the velocity function by taking the first derivative and the acceleration by taking the second derivative.<br />
10. 10. Characteristics of Graphs<br />
11. 11. Using the first and second derivative of graphs, you can find characteristics of the original graph such as when it is increasing/decreasing, local maxs/mins, concavity intervals, and points of inflection.<br />