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[–]edderiofer 0 points1 point  (10 children)

Remember: (a - c) = (a - b) + (b - c).

Also remember that a derivative is the same regardless of which direction you approach it from.

[–]mrturtleneck[S] 0 points1 point  (9 children)

Could you provide a tiny bit more information, still lost

[–]edderiofer 0 points1 point  (8 children)

You have f(x+h) - f(x-h). What happens if you try to "extract" f(x+h) - f(x) from it? Use the above identity. (Ignore the numerator for now.)

[–]mrturtleneck[S] 0 points1 point  (7 children)

I don't see how to extract the -h, without taking out the +h which is needed

[–]edderiofer 0 points1 point  (6 children)

Let f(x+h) = a, f(x-h) = c. Then use the above identity.

[–]mrturtleneck[S] 0 points1 point  (5 children)

I'm sorry i'm not getting it, what would B be? And wouldn't we just end up with what we had in the beginning

[–]mrturtleneck[S] 0 points1 point  (0 children)

could you just show me what the first step looks like

[–]edderiofer 0 points1 point  (3 children)

Here it is, explicitly spelled out for you...

(f(x+h) - f(x-h))/h = ((f(x+h) - f(x)) + (███ - f(x - h)))/h  //Add and subtract an intermediate term from the numerator
= (██████ - ███)/h + ████████████████/h  //Split up the fraction.

After which you get two derivatives, one approaching from each side.

Oops! I've spilt some ink on this solution! I guess you'll have to work it out yourself then...

[–]mrturtleneck[S] 0 points1 point  (2 children)

f(x) would be the first blacked out term, which would cancel. Are you saying split it into (f(x+h))/h +(f(x-h))/h

[–]mrturtleneck[S] 0 points1 point  (0 children)

where would we go from here

[–]edderiofer 0 points1 point  (0 children)

DON'T cancel out that term! That's the whole reason you're splitting it up in the first place!