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onegirl

  • 2 years ago

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

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  1. onegirl
    • 2 years ago
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  2. satellite73
    • 2 years 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
    • 2 years ago
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    okay can u show it?

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

  5. onegirl
    • 2 years ago
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    @zepdrix can u help?

  6. zepdrix
    • 2 years 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
    • 2 years ago
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    ok

  8. zepdrix
    • 2 years 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
    • 2 years ago
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    okay

  10. zepdrix
    • 2 years 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
    • 2 years ago
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    okay

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

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

  14. onegirl
    • 2 years ago
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    0

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

  16. onegirl
    • 2 years ago
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    okay

  17. zepdrix
    • 2 years 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
    • 2 years ago
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    okay

  19. zepdrix
    • 2 years 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
    • 2 years ago
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    Ok let's draw a line connecting these points.

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

  22. onegirl
    • 2 years ago
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    okay that makes sense now

  23. zepdrix
    • 2 years ago
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    So how about the second derivative. Hmmm

  24. onegirl
    • 2 years ago
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    it will be horizontal

  25. zepdrix
    • 2 years ago
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    |dw:1362595623497:dw|

  26. zepdrix
    • 2 years 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
    • 2 years ago
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    yes

  28. zepdrix
    • 2 years 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
    • 2 years ago
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    ok

  30. zepdrix
    • 2 years 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
    • 2 years ago
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    okay thanks

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