Show that $f(x)$ cannot be zero
6166
Is the following statement provable?
154360
Show $f$ can't be irreducible over a finite field if $f^\prime$ is the zero polynomial.
2717
Help proving existence of an specific $x_0$ for which $f''(x_0)=0$
8854
Prove $f $ is identically zero if $f(0)=0$ and $|f'(x)|\le|f(x)|$
82001
How to prove the function is a constant
143491
Show that $f$ is differentiable on $(−1, 1)$.
70458
Show that it is possible that the limit $\displaystyle{\lim_{x \rightarrow +\infty} f'(x)} $ does not exist.
122762
Proving that the limit doesn't exist for $x$ other than $0$
54729
Prove that $f$ has a fixed point .
112285
Show that $\lim_{x\to\infty} f(x)=0 \implies \lim_{x\to\infty} f'(x)=0$
83338
Show that there's no continuous function that takes each of its values $f(x)$ exactly twice.
128766
Show that the set of functions $\mathbb{N}\to\{0,1\}$ is not countable
13533
Proof that the limit of $\frac{1}{x}$ as $x$ approaches $0$ does not exist
118873
Prove that $f(x)=0$ for all $x\in\mathbb{R}$.
66951
Proving the existence of a sequence of functions converging to 0 with an added property
11322
Show that $f$ vanishes identically.
18153
To prove that $f_n(x) = \frac{nx}{1+n^2x^2}$ does not uniformly converge to $f(x) = 0$ on $[0,1]$