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onegirl

  • one year ago

Draw the second derivative given the graph of function f below.

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  1. onegirl
    • one year ago
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  2. satellite73
    • one year ago
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    first derivative of a parabola is probably a line second derivative will therefore be a constant, aka a horizontal line

  3. onegirl
    • one year ago
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    okay can u show it?

  4. onegirl
    • one year ago
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    |dw:1362594670556:dw| how will i draw it on here?

  5. onegirl
    • one year ago
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    @zepdrix can u help?

  6. zepdrix
    • one year ago
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    |dw:1362595003756:dw|Let's draw some tangent lines to get a feel for what is going on

  7. onegirl
    • one year ago
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    ok

  8. zepdrix
    • one year ago
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    |dw:1362595106001:dw|See how the SLOPE of the porabola is very negative on the left? The line is pointing downward, very negative. That line has a bad attitude! XD That is telling us that the VALUE of our first derivative will be very negative. I've drawn a point near the bottom to show this.

  9. onegirl
    • one year ago
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    okay

  10. zepdrix
    • one year ago
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    |dw:1362595210278:dw|Check out this tangent line. It's still pointing downward, but not as much as the last one. It has a less negative slope. So our first derivative will have a negative value, but not as negative as the first point.

  11. onegirl
    • one year ago
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    okay

  12. zepdrix
    • one year ago
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    |dw:1362595320296:dw|How about this tangent line, what is it's value?

  13. zepdrix
    • one year ago
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    what is the slope of this tangent line i mean*

  14. onegirl
    • one year ago
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    0

  15. zepdrix
    • one year ago
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    |dw:1362595394811:dw|yes good. so the VALUE of our derivative will be 0.

  16. onegirl
    • one year ago
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    okay

  17. zepdrix
    • one year ago
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    |dw:1362595424698:dw|When we go towards the right, the slope becomes positive. So our point will be somewhere up in the positive area.

  18. onegirl
    • one year ago
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    okay

  19. zepdrix
    • one year ago
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    |dw:1362595476831:dw|As we go further to the right, our slope gets really positive, so the value of the first derivative will be very positive.

  20. zepdrix
    • one year ago
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    Ok let's draw a line connecting these points.

  21. zepdrix
    • one year ago
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    |dw:1362595554967:dw|I had to fix a couple of the dots :) lol

  22. onegirl
    • one year ago
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    okay that makes sense now

  23. zepdrix
    • one year ago
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    So how about the second derivative. Hmmm

  24. onegirl
    • one year ago
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    it will be horizontal

  25. zepdrix
    • one year ago
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    |dw:1362595623497:dw|

  26. zepdrix
    • one year ago
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    Yes good! Because the slope of this line is constant yes? If we were to check points, we would see that the tangent lines are all giving us the same slope.

  27. onegirl
    • one year ago
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    yes

  28. zepdrix
    • one year ago
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    With the way I've drawn this particular first derivative, it has a slope of approximately 1. So our second derivative would have a VALUE of 1.|dw:1362595735329:dw|

  29. onegirl
    • one year ago
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    ok

  30. zepdrix
    • one year ago
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    Just make sure that you draw your second derivative ABOVE the x-axis. That shows that the first derivative was positive.

  31. onegirl
    • one year ago
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    okay thanks

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