anonymous
  • anonymous
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?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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Michele_Laino
  • Michele_Laino
what is: E^2x
anonymous
  • anonymous
I just made it up.. how about E^x
anonymous
  • anonymous
\[f'[x]=(x+2)/E^x\]

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Michele_Laino
  • Michele_Laino
we can integrate yor first derivative, nevertheless I don't know how, since I don't know the meaning of E^x
anonymous
  • anonymous
is that not E to the power of x?
Michele_Laino
  • Michele_Laino
yes! Is E the base of natural logarithms
anonymous
  • anonymous
yes
anonymous
  • anonymous
So I would need to integrate.. I haven't learned that yet.. I guess that's coming next..
Michele_Laino
  • Michele_Laino
ok! then we have to compute this integral: \[\Large \int {\left( {x + 2} \right){e^{ - x}}} dx\]
Michele_Laino
  • Michele_Laino
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
Michele_Laino
  • Michele_Laino
in other words you have a family of functions, which differ each other by an additive constant C |dw:1435230843014:dw|
Michele_Laino
  • Michele_Laino
where: \[\Large f\left( x \right) = - {e^{ - x}}\left( {x + 3} \right)\]
anonymous
  • anonymous
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.
Michele_Laino
  • Michele_Laino
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
anonymous
  • anonymous
ahh right.. d/dx C would be 0 so you would have a number of potential functions
Michele_Laino
  • Michele_Laino
that's right!
anonymous
  • anonymous
ah well, then hopefully the problem has at least one point defined.. like 0,1
anonymous
  • anonymous
and we restrict the family.
Michele_Laino
  • Michele_Laino
yes! that's right!
anonymous
  • anonymous
cool, thanks michele..
Michele_Laino
  • Michele_Laino
:)

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