query: Show that $f'(x) = f^2(x)$ and $f(0) = 0$ implies $f$ is the zero function
positive_passages.docid: 69008
positive_passages.text: $f'(x) = [f(x)]^{2}$. Prove $f(x) = 0 $
negative_passages.docid: 90369
negative_passages.text: Does $\int_a^bf(x) = 0$ imply $f(x) = 0$ for a Riemann Integral function?
negative_passages.docid: 95288
negative_passages.text: Prove that, $f'(0) \ge -\sqrt{2}$ for a function $f$ satisfying some conditions on $(-1,1)$.
negative_passages.docid: 147325
negative_passages.text: Proving that if $f(x)=x$ has no real solution then $f(f(x))=x$ has no real solution either
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: 107795
negative_passages.text: If $\,f''(x) \ge f(x)$, for all $x\in[0,\infty),$ and $\,f(0)=f'(0)=1$, then is $\,f(x)>0$?
negative_passages.docid: 10428
negative_passages.text: Proving that $\lim\limits_{x\to\infty}f'(x) = 0$ when $\lim\limits_{x\to\infty}f(x)$ and $\lim\limits_{x\to\infty}f'(x)$ exist
negative_passages.docid: 35889
negative_passages.text: Suppose that f(0) = f(1) = 0 and x ∈ (0, 1). Prove that there exists c ∈ (0, 1) such that f'(c) = f(x).
negative_passages.docid: 88271
negative_passages.text: Prove the exsistence of 3 zero points of a function
negative_passages.docid: 131000
negative_passages.text: A proof of a criterion of vanishing of a function.
negative_passages.docid: 85739
negative_passages.text: Show that $f(x) = 0$ for all $x \in [a,b]$ given $|f'(x)| \leq C|f(x)| $
negative_passages.docid: 89537
negative_passages.text: $ \int_0^x f(t)dt=\int_0^{ax}f(t)dt+ \int_0^{bx}f(t)dt$ implies $f$ constant
negative_passages.docid: 76311
negative_passages.text: $f'' + f =0$: finding $f$ using power series
negative_passages.docid: 59063
negative_passages.text: $f(f(x))=f(x)$ question
negative_passages.docid: 100765
negative_passages.text: If $f'(x) = 0$ for all $x \in \mathbb{Q}$, is $f$ constant?
negative_passages.docid: 138544
negative_passages.text: For which values of $x$, will $f (x) . f '(x) < 0$?
negative_passages.docid: 9270
negative_passages.text: Differentiable function, with $f'(x)=[f(x)]^2$