Second derivative question

1. The problem statement, all variables and given/known data

Show that lim(h-->0) [f(x+h)-2f(x) + f(x-h)]/h^2
is equal to f''(x) for any given value of x where the second derivative exists.

I'm supposed to use L'Hopitals rule for this problem. I did and got

Now I am stuck. I thought about adding and subtracting say f(x) but don't see how that solves to f''(x)


Homework Helper
You're almost there. You can rewrite that as the average of the left and right limits for the derivative of f(x), which will be the same if f is differentiable at x.


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is not the derivative of

f(x+h)-2f(x) + f(x-h)

p.s.: for the record, you have to assume f is differentiable in an entire neighborhood of x in order to invoke L'Hôpital's rule.
Last edited:

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