Let f : R→R be a non-constant , three times differentiable function. If f(1+1/n)=1 for all integers , then f''(1) equals? I don't even know how to start this problem!
2026-03-25 04:36:31.1774413391
Finding the differential of a thrice differentiable function
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HINT: Can you start by finding $f'(1)$ by using the sequence $1+1/n\to 1$ ($n\to\infty$)? Now consider either the second-order Taylor polynomial of $f$ at $1$ or a formula for $f''(a)$ using $a+h$, $a$, and $a-h$.
Comment: I'm not sure why you need $f$ to be three-times differentiable.