Comment on the monotonicity of $g(x)={f(x)\over x}$
33523
If $f(0)=0$ and $f'$ is increasing, then $\frac{f(x)}{x}$ is increasing.
13852
Assume $f$ is a continuous one-to-one function over an interval. Prove that $f$ is strictly monotone
65033
Prove inverse of strictly monotone increasing function is continuous over the range of original function
43956
Differentiating $f(x)^{g(x)}$
70128
Prove that $(fg)^{(n)} = \sum_{k=0}^n \binom{n}{k}f^{(k)}(x)g^{(n-k)}(x)$
110313
Prove that $\gcd(f(x),g(x)) = 1$.
104848
What's the name of this theorem ($f>g$ given $f'>g'$ and initial value)?
93806
$\|f\|_{L^{p}}=\sup\left\{\int_{{\bf R}^{n}}|f(x)g(x)|~dx:\|g\|_{L^{q}}\le1\right\}$
103801
$xT=x$ iff $x=e$ implies that every $g$ may be written as $x^{-1}(xT)$ for some $x\in G$.
89473
Uniqueness of minimal polynomial: $f(x)$ divides $g(x)$
144589
Proving that if $f(x) \le g(x)$ then $f(x_0) \le g(x_0)$
40609
Prove that $f(X)$ and $g(Y)$ are independent if $X$ and $Y$ are independent
158282
Finite order of an element $f(g)$ of a homomorphism $f$
145265
A non-zero function satisfying $g(x+y) = g(x)g(y)$ must be positive everywhere
6450
Show $\mathbb{E}[f(X)g(X)] \geq \mathbb{E}[f(X)]\mathbb{E}[g(X)]$ for $f,g$ bounded, nondecreasing
68048
Prove that if $f$ is differentiable on $[a,b]$ and $f'$ is monotonic on $[a,b]$ , $f'$ is continuous on $[a,b]$
7858
Proving that $f(x)$ is irreducible over $F(b)$ if and only if $g(x)$ is irreducible over $F(a)$