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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?
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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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I just made it up.. how about E^x

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.4we can integrate yor first derivative, nevertheless I don't know how, since I don't know the meaning of E^x

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0is that not E to the power of x?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.4yes! Is E the base of natural logarithms

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So I would need to integrate.. I haven't learned that yet.. I guess that's coming next..

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.4ok! then we have to compute this integral: \[\Large \int {\left( {x + 2} \right){e^{  x}}} dx\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.4after 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
 one year ago
Best ResponseYou've already chosen the best response.4in other words you have a family of functions, which differ each other by an additive constant C dw:1435230843014:dw

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.4where: \[\Large f\left( x \right) =  {e^{  x}}\left( {x + 3} \right)\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so 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
 one year ago
Best ResponseYou've already chosen the best response.4better 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
 one year ago
Best ResponseYou've already chosen the best response.0ahh right.. d/dx C would be 0 so you would have a number of potential functions

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ah well, then hopefully the problem has at least one point defined.. like 0,1

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0and we restrict the family.

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.4yes! that's right!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0cool, thanks michele..
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