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I'm having trouble placing the concepts and possiblities of the to be introduced F# language from Microsoft.
Will F# be used just for declaring functions? Or will applications be written 'entirely' in F# by mixing F# together with normal C# or VB code?
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To our common sense, when f is always greater than o, then the function is always above x-axis, and when f is always less than 0, f is always below the x-axis. And if f is just greater than 0 at certain range, then it is just above x-axis at that corresponding range, vise versa.
more ... A special relationship where each input has a single output. It is often written as "f(x)" where x is the input value. Example: f(x) = x/2 ("f of x equals x divided by 2")
Remember: The notation "f (x)" is exactly the same thing as "y". You can even label the y-axis on your graphs with "f (x)", if you feel like it.
The derivative of a function f(x) is the function whose value at x is f′(x). The graph of a derivative of a function f(x) is related to the graph of f(x). Where f(x) has a tangent line with positive slope, f′(x)>0. Where f(x) has a tangent line with negative slope, f′(x)<0.
I can highly recommend you to watch Luca Bolognese's talk from PDC 2008. It's not only very entertaining but he also demonstrates quite impressive use cases of F#:
An Introduction to Microsoft F# by Luca Bolognese
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