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Concavity and Inflection Points

Concavity and Inflection Points. The second derivative will show where a function is concave up or concave down. It is also used to locate inflection points. Concavity and Inflection Points.

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Concavity and Inflection Points

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  1. Concavity and Inflection Points The second derivative will show where a function is concave up or concave down. It is also used to locate inflection points.

  2. Concavity and Inflection Points The second derivative will show where a function is concave up or concave down. It is also used to locate inflection points. Concave up – this occurs as the slope of the tangent line increases

  3. Concavity and Inflection Points The second derivative will show where a function is concave up or concave down. It is also used to locate inflection points. Concave up – this occurs as the slope of the tangent line increases - As you can see, as I move from LEFT to RIGHT, the tangent line goes from a ( - ) value to a ( + ) value…

  4. Concavity and Inflection Points The second derivative will show where a function is concave up or concave down. It is also used to locate inflection points. Concave up – this occurs as the slope of the tangent line increases - As you can see, as I move from LEFT to RIGHT, the tangent line goes from a ( - ) value to a ( + ) value… Concave down – this occurs as the slope of the tangent line decreases - As you can see, as I move from LEFT to RIGHT, the tangent line goes from a ( + ) value to a ( - ) value…

  5. Concavity and Inflection Points The second derivative will show where a function is concave up or concave down. It is also used to locate inflection points. Concave up – this occurs as the slope of the tangent line increases Concave down – this occurs as the slope of the tangent line decreases

  6. Concavity and Inflection Points The second derivative will show where a function is concave up or concave down. It is also used to locate inflection points. Concave up – this occurs as the slope of the tangent line increases Concave down – this occurs as the slope of the tangent line decreases

  7. Concavity and Inflection Points The second derivative will show where a function is concave up or concave down. It is also used to locate inflection points. Inflection Point – occur where a graph changes from concave up to concave down, or vice versa

  8. Concavity and Inflection Points The second derivative will show where a function is concave up or concave down. It is also used to locate inflection points. Inflection Point – occur where a graph changes from concave up to concave down, or vice versa

  9. Concavity and Inflection Points The second derivative will show where a function is concave up or concave down. It is also used to locate inflection points. Inflection Point – will occur where a graph changes from concave up to concave down, or vice versa Inflection point

  10. Concavity and Inflection Points

  11. Concavity and Inflection Points

  12. Concavity and Inflection Points

  13. Concavity and Inflection Points 1 0 2. Set up your intervals

  14. Concavity and Inflection Points 1 0 2. Set up your intervals

  15. Concavity and Inflection Points 2. Set up your intervals

  16. Concavity and Inflection Points 2. Set up your intervals - place on number line

  17. Concavity and Inflection Points 2. Set up your intervals

  18. Concavity and Inflection Points CU 2. Set up your intervals Concave up

  19. Concavity and Inflection Points CU CU 2. Set up your intervals Concave up Concave up

  20. Concavity and Inflection Points CU CD CU 2. Set up your intervals Concave up Concave up Concave down

  21. Concavity and Inflection Points CU CD CU CD 2. Set up your intervals Concave up Concave up Concave down Concave down

  22. Concavity and Inflection Points

  23. Concavity and Inflection Points

  24. Concavity and Inflection Points 2. Set up your intervals

  25. Concavity and Inflection Points 2. Set up your intervals

  26. Concavity and Inflection Points 2. Set up your intervals - place on number line ** yes, it is possible that a critical point will also be an inflection point

  27. Concavity and Inflection Points 2. Set up your intervals

  28. Concavity and Inflection Points CU 2. Set up your intervals Concave up

  29. Concavity and Inflection Points CU CD 2. Set up your intervals Concave up Concave down

  30. Concavity and Inflection Points CU CD CU 2. Set up your intervals Concave up Concave down Concave up

  31. Concavity and Inflection Points CU CD CU CU 2. Set up your intervals Concave up Concave down Concave up Concave up

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