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anonymous

  • one year ago

If you only had a derivative of a function, and you had to work out what the plot of the original curve was, and maybe the derivative too, how would you approach that problem?

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  1. Michele_Laino
    • one year ago
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    what is: E^2x

  2. anonymous
    • one year ago
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    I just made it up.. how about E^x

  3. anonymous
    • one year ago
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    \[f'[x]=(x+2)/E^x\]

  4. Michele_Laino
    • one year ago
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    we can integrate yor first derivative, nevertheless I don't know how, since I don't know the meaning of E^x

  5. anonymous
    • one year ago
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    is that not E to the power of x?

  6. Michele_Laino
    • one year ago
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    yes! Is E the base of natural logarithms

  7. anonymous
    • one year ago
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    yes

  8. anonymous
    • one year ago
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    So I would need to integrate.. I haven't learned that yet.. I guess that's coming next..

  9. Michele_Laino
    • one year ago
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    ok! then we have to compute this integral: \[\Large \int {\left( {x + 2} \right){e^{ - x}}} dx\]

  10. Michele_Laino
    • one year ago
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    after a simple computation, we get: \[\Large \int {\left( {x + 2} \right){e^{ - x}}} dx = - {e^{ - x}}\left( {x + 3} \right) + C\] where C is the usually arbitrary real constant

  11. Michele_Laino
    • one year ago
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    in other words you have a family of functions, which differ each other by an additive constant C |dw:1435230843014:dw|

  12. Michele_Laino
    • one year ago
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    where: \[\Large f\left( x \right) = - {e^{ - x}}\left( {x + 3} \right)\]

  13. anonymous
    • one year ago
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    so now its just a matter of plotting the functions out.. or working out the points.. thank you michele, I was just curious on this one.. I need to read up on the rules for integration.

  14. Michele_Laino
    • one year ago
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    better is if you draw the graph of the function: \[\Large f\left( x \right) = - {e^{ - x}}\left( {x + 3} \right)\] applying the theorems of Mathematical Analysis. Once you got that graph, you only shift it up or down by an arbitrary constant C, so you will get a family of functions, whose first derivative is given by the derivative which you provided

  15. anonymous
    • one year ago
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    ahh right.. d/dx C would be 0 so you would have a number of potential functions

  16. Michele_Laino
    • one year ago
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    that's right!

  17. anonymous
    • one year ago
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    ah well, then hopefully the problem has at least one point defined.. like 0,1

  18. anonymous
    • one year ago
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    and we restrict the family.

  19. Michele_Laino
    • one year ago
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    yes! that's right!

  20. anonymous
    • one year ago
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    cool, thanks michele..

  21. Michele_Laino
    • one year ago
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    :)

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