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anonymous

  • one year ago

The graph of y = f ′(x), the derivative of f(x), is shown below. Given f(2) = 8, evaluate f(–2).

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  1. anonymous
    • one year ago
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  2. anonymous
    • one year ago
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    let me try to do it on my own,tell me if i'm doing something wrong

  3. anonymous
    • one year ago
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    Sure

  4. anonymous
    • one year ago
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    Remember, use the information that f(2)=8, to find f(-2)

  5. anonymous
    • one year ago
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    |dw:1439294446810:dw|

  6. anonymous
    • one year ago
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    that feels wrong

  7. anonymous
    • one year ago
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    Hmm, you don't need that graph at all

  8. anonymous
    • one year ago
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    okay i have no idea where to start :/

  9. anonymous
    • one year ago
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    Look at the middle line segment, going from (-2,-2,) to (2,2) is the line segment you need to look at

  10. anonymous
    • one year ago
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    okay is the answer 8?

  11. anonymous
    • one year ago
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    im saying 8 only because the graph seems mirrored and if it

  12. anonymous
    • one year ago
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    Idk, I haven't calculated the answer yet use the formula \[\int\limits_{-2}^{2}f'(x)dx=f(2)-f(-2)\] \[f(-2)=f(2)-\int\limits_{-2}^{2}f'(x)dx=8-\int\limits_{-2}^{2}y.dx\] Have you studied about the definite integral?

  13. anonymous
    • one year ago
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    okay that seems way better, one sec

  14. anonymous
    • one year ago
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    and yes i have

  15. anonymous
    • one year ago
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    Good, you need to find y(x) for the interval -2 to 2, it will be the equation of the middle line segment, again since it's passing through origin it's c will be 0 \[y=mx+c=mx+0=mx=(\frac{y_{2}-y_{1}}{x_{2}-x_{1}})x\] m=slope (x1,y1) (x2,y2) are any points on the line segment

  16. anonymous
    • one year ago
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    x

  17. anonymous
    • one year ago
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    so y = x?

  18. anonymous
    • one year ago
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    yes!! y=x \[f(-2)=8-\int\limits_{-2}^{2}x.dx\] Now it's a simple matter of integration

  19. anonymous
    • one year ago
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    8!!

  20. anonymous
    • one year ago
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    I LOVE YOU!!

  21. ganeshie8
    • one year ago
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    Hey! allternatively we could also use the symmetry to conclude that the integral is 0

  22. anonymous
    • one year ago
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    good job jeb!!

  23. anonymous
    • one year ago
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    -_- how did i not see that

  24. anonymous
    • one year ago
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    Oh yeah, the same amount of area under the line is negative as it is positive so it cancels out

  25. anonymous
    • one year ago
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    oh well it doesn't matter i get it! :D

  26. ganeshie8
    • one year ago
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    |dw:1439295272579:dw|

  27. anonymous
    • one year ago
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    but it is also important that you know the method

  28. anonymous
    • one year ago
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    thanks so much guys, i should probably head to bed its 5:20 am here

  29. anonymous
    • one year ago
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    anyway thanks again!

  30. ganeshie8
    • one year ago
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    Another alternative, Since \(f'(x)\) is an odd function, it follows that \(f(x)\) is an even function. Therefore \(f(-2)=f(2)=8\)

  31. anonymous
    • one year ago
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    amazing

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