Let $f$ be a continuous differential function on $(0,\infty)$ with $f(0)=0$ and that $f'$ is increasing on $(0,\infty)$
33523
If $f(0)=0$ and $f'$ is increasing, then $\frac{f(x)}{x}$ is increasing.
50472
If monotone decreasing and $\int_0^\infty f(x)dx <\infty$ then $\lim\limits_{x\to\infty} xf(x)=0.$
114747
If $\lim_{x \to \infty}f'(x)=+\infty$ then $\lim_{x \to \infty}(f(x)-f(x-1))=+\infty$ and $\lim_{x \to \infty}f(x)=+\infty$.
2717
Help proving existence of an specific $x_0$ for which $f''(x_0)=0$
90892
Is a function increasing if the derivative is positive except at one point of an interval?
10428
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
34187
The limit of the derivative of an increasing and bounded function is always $0$?
78319
Show that $x \mapsto \frac{f(x)}{x}$ is strictly increasing on (0,1) given that f '(x) is strictly increasing on (0,1) and that f(0)=0
135999
One sided limit of an increasing function defined on an open interval
112211
Show an increasing function f from omega_1 to R is eventually constant
105068
Proving that the function is differentiable and $f'(0)=0$
10747
Given function $g$ continuous in line $[0,\infty)$...
50103
Show that a continuous function satisfying $f(2^x)=f(3^x)$ for $x\in (0,\infty)$ is a constant function
129579
If $f''(x_0)$ exists then $\lim_{x \to x_0} \frac{f(x_0+h)-2f(x_0)+f(x_0-h)}{h^2} = f''(x_0)$
37303
Differential of a smooth function
154881
Question on differentiability of a continuous function
15727
show that if $f$ is uniformly differentiable then prove that $f'$ is continuous