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farmergirl411

  • 2 years ago

I need help figuring out how the derivative of the graph would look approximatially.

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  1. farmergirl411
    • 2 years ago
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    |dw:1362964903781:dw|

  2. farmergirl411
    • 2 years ago
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    This is the original graph how would the derivative look

  3. ahdreaonna
    • 2 years ago
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    rigth

  4. ahdreaonna
    • 2 years ago
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    so

  5. zepdrix
    • 2 years ago
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    |dw:1362965404144:dw|These are the easy points to start with. Draw tangent lines. See how the slope of these tangent lines is 0. That means the VALUE of the derivative function will be zero.

  6. zepdrix
    • 2 years ago
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    |dw:1362965478556:dw|

  7. farmergirl411
    • 2 years ago
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    so then the derivative just goes along the x line

  8. zepdrix
    • 2 years ago
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    No, the derivative passes through the x-axis at those 3 points :) now let's find some other points.

  9. farmergirl411
    • 2 years ago
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    ok

  10. zepdrix
    • 2 years ago
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    |dw:1362965586761:dw|Understand how I drew the line tangent to the curve? See how it's pointing downward (read from left to right). It has an extremely negative slope. Meaning the derivative function will have an extremely negative VALUE at this x coordinate.

  11. zepdrix
    • 2 years ago
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    |dw:1362965677365:dw|

  12. farmergirl411
    • 2 years ago
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    ok

  13. ahdreaonna
    • 2 years ago
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    well then there you ave it

  14. zepdrix
    • 2 years ago
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    |dw:1362965734778:dw|Now the function is starting to come together! c:

  15. zepdrix
    • 2 years ago
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    Have you learned about inflection points? :o Is this all too confusing farmergal? :c

  16. farmergirl411
    • 2 years ago
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    no so then does it just go up to the x line then hit the dots on the x line.

  17. zepdrix
    • 2 years ago
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    Yes, but it will keep going past the x line, how far? Well until we reach the inflection point.

  18. farmergirl411
    • 2 years ago
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    Now I'm confussed when you say it keeps going to the inflection point.

  19. zepdrix
    • 2 years ago
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    |dw:1362965901972:dw|Right around that point, it changes from `Concave Up` to `Concave Down`.

  20. farmergirl411
    • 2 years ago
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    |dw:1362965979553:dw|SO it will look like this

  21. zepdrix
    • 2 years ago
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    |dw:1362965980976:dw|

  22. zepdrix
    • 2 years ago
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    Ummmm yah it looks like that's where we're headed :)

  23. farmergirl411
    • 2 years ago
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    ok I got it so far.

  24. zepdrix
    • 2 years ago
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    |dw:1362966105601:dw|

  25. farmergirl411
    • 2 years ago
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    ok

  26. zepdrix
    • 2 years ago
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    |dw:1362966148110:dw|So at that x coordinate, our derivative function reaches the bottom of the bowl :D

  27. farmergirl411
    • 2 years ago
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    ok go it

  28. zepdrix
    • 2 years ago
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    |dw:1362966245521:dw|If we check one last point way on the right over here, it appears to be very positive slope, so the derivative function will have a very positive value.

  29. zepdrix
    • 2 years ago
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    |dw:1362966295539:dw|

  30. zepdrix
    • 2 years ago
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    Something like that, the original graph was a tad sloppy. So it's hard to say for certain :) heh

  31. farmergirl411
    • 2 years ago
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    ok got it thanks

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