$f(x)$ decreasing and positive implies $f'(x)$ converges to 0?
34187
The limit of the derivative of an increasing and bounded function is always $0$?
88147
Show that $g_n(x)=nf(x+1/n)-nf(x)$ converges uniformly to $f'$
114702
$\int_0^{\infty} f(x)dx$ converges and $\lim_{x\rightarrow \infty} f(x)$ exists, then $\lim_{x\rightarrow \infty} f(x)=0$?
121771
Proof $f(x)\equiv 0$
23864
Rolle's theorem $\beta \cdot f(x)+f'(x)=0$
69008
$f'(x) = [f(x)]^{2}$. Prove $f(x) = 0 $
110415
Proving a sequence of step functions converges pointwise to a function $f$.
813
$f$ uniformly continuous and $\int_a^\infty f(x)\,dx$ converges imply $\lim_{x \to \infty} f(x) = 0$
117906
Show that $\liminf\limits_{x\to \infty}|f'(x)|=0$ if $\lim\limits_{x\to \infty}f(x)/x=0$ and $f$ is differentiable
28949
Prove $f(x) = 0 $for all $x \in [0, \infty)$ when $|f'(x)| \leq |f(x)|$
41037
Prove that $f'(a)=\lim_{n\to\infty}\frac{f(b_n)-f(a_n)}{b_n-a_n}$ under some conditions
120406
$f$ strictly increasing does not imply $f'>0$
153063
Uniform convergence of $f_n(x)=nx^n(1-x)$ for $x \in [0,1]$?
74583
Prove that $f'(0)=L$.
136980
Prove there exists $a\in \Bbb{R}$ such that $f'(a)=0$.
88311
Linear functional f(v)=0 imply v=0
35091
How can I prove this sequence is decreasing?