Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Show that, for a twice differentiable function $f$, $$\lim_{h\to 0} \frac{f(a+2h)-2f(a+h)+f(a)}{h^2} = f''(a)$$

share|improve this question
Unfortunately your recent string of questions has the look of you posting a problem set in a course. Could you slow down a bit, concentrate on one question at a time, and tell us (i) in what context these questions are arising and (ii) what thoughts you have had / work you have done on them already? –  Pete L. Clark May 16 '12 at 22:04
add comment

1 Answer 1

f '(x) = lim h->0 [f(x + h)) - f(x)]/h

Now following the same formula for f''(a) except now instead of lim h->0 [f(x + h) - f(x)]/h, you use:

lim h->0 [f '(a + h) - f '(a)]/h

f "(a) = lim h->0 [f(a + 2h) - f(a + h)]/h - [f(a + h) - f(a)]/h

= lim h->0 [f(a + 2h) - 2*f(a + h) + f(a)]/h

share|improve this answer
Given Pete Clark's comment above, you should know that giving an answer to this ill-formulated question is not helping the OP. –  M Turgeon May 29 '12 at 17:33
gurl, check out meta.math.stackexchange.com/questions/107/… and en.wikipedia.org/wiki/… to find out how to typeset formulas nicely here –  Yrogirg May 30 '12 at 12:05
add comment

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.