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?

Question

michele_laino · Answer

what is:
E^2x

anonymous · Answer

I just made it up.. how about E^x

anonymous · Answer

$$f'[x]=(x+2)/E^x$$

michele_laino · Answer

we can integrate yor first derivative, nevertheless I don't know how, since I don't know the meaning of E^x

anonymous · Answer

is that not E to the power of x?

michele_laino · Answer

yes! Is E the base of natural logarithms

anonymous · Answer

yes

anonymous · Answer

So I would need to integrate.. I haven't learned that yet.. I guess that's coming next..

michele_laino · Answer

ok! then we have to compute this integral:
$$\Large  \int {\left( {x + 2} \right){e^{ - x}}} dx$$

michele_laino · Answer

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 · Answer

in other words you have a family of functions, which differ each other by an additive constant C
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