query: If $f: R \to R$ is a non constant, thrice differentiable function such that $f(1+ \frac{1}{n}) = 1$ for all integers, then find $f''(1)$
positive_passages.docid: 144323
positive_passages.text: Differentiation of a function
negative_passages.docid: 142682
negative_passages.text: Find $f(x)$ where $ f(x)+f\left(\frac{1-x}x\right)=x$
negative_passages.docid: 143491
negative_passages.text: Show that $f$ is differentiable on $(−1, 1)$.
negative_passages.docid: 30855
negative_passages.text: Finding all differentiable $f(z) = u(x) + iv(y)$ in $\mathbb{C}$ where $u(x),v(y)$ are real valued functions.
negative_passages.docid: 8179
negative_passages.text: If $f$ is entire and $|f|\geq 1$, then show $f$ is constant.
negative_passages.docid: 4636
negative_passages.text: How to show that $f$ is differentiable at $x=0.$
negative_passages.docid: 144222
negative_passages.text: If $f(x + 1) + f(x − 1) = f(x), \forall x \in \mathbb{R}$,then how to find $k$ such that $f(x + k) = f(x)$?
negative_passages.docid: 135199
negative_passages.text: Looking for a function $f$ that is $n$-differentiable, but $f^{(n)}$ is not continuous
negative_passages.docid: 34790
negative_passages.text: Find $f(1)$ from equation $\int_{0}^{x}f(t)dt = x+\int_{x}^{1}tf(t)dt$
negative_passages.docid: 48275
negative_passages.text: $f$ defined $|f(x) - f(y)| \leq |x - y|^{1+ \alpha}$ Prove that $f$ is a constant.
negative_passages.docid: 98255
negative_passages.text: Find $f(x)$ such that $f(f(x)) = x^2 - 2$
negative_passages.docid: 33523
negative_passages.text: If $f(0)=0$ and $f'$ is increasing, then $\frac{f(x)}{x}$ is increasing.
negative_passages.docid: 9587
negative_passages.text: If $f(t) = 1+ \frac{1}{2} +\frac{1}{3}+....+\frac{1}{t}$, find $\sum^n_{r=1} (2r+1)f(r)$ in terms of $f(n)$
negative_passages.docid: 135693
negative_passages.text: Suppose f is a twice differentiable function with $f(0)=0$ and $f(1)=1$, $f'(0)=f'(1)=0$. Then show that $|f''(x)| > 4$ for some $x$ in $(0,1)$
negative_passages.docid: 129324
negative_passages.text: Let $f:[0;1]\to\mathbb R$ be continiously differentiable
negative_passages.docid: 82001
negative_passages.text: How to prove the function is a constant
negative_passages.docid: 77581
negative_passages.text: Let $f(x)$ be differentiable at $\mathbb R$, s.t $|f^\prime (x)| \le 6$ . Its given that $f(1)=20$, and $f(9)=68$ , prove that $f(7)=56$.