If $f(x) \geq 0$, then $g(x) =f(x)+f'(x)+f''(x)+...+f^r(x) \geq 0$
1519
Sum of derivatives of a polynomial
105319
A calculus problem with functions such that $f''(x) = g(x)$ and $g''(x) = f(x)$
5419
Continuous functions with $f^2(x)=g^2(x)\neq 0$
94564
If $f$ is bounded and $\lim_{x \to c} g(x) = 0$, then $\lim_{x \to c}g(x)f(x) = 0$
119042
If $f+g$ and $f$ are differentiable at $a$, must $g$ be differentiable at $a$?
98399
Suppose $f$ and $g$ are entire functions, and $|f(z)| \leq |g(z)|$ for all $z \in \mathbb{C}$, Prove that $f(z)=cg(z)$.
28949
Prove $f(x) = 0 $for all $x \in [0, \infty)$ when $|f'(x)| \leq |f(x)|$
81720
$f(x) + f(x+f(y)) = y + f(f(x) + f(f(y)))$
121455
$f(x)$ if $f(xy)=f(x) +f(y) +\frac{x+y-1}{xy}$
33523
If $f(0)=0$ and $f'$ is increasing, then $\frac{f(x)}{x}$ is increasing.
57026
$f(0)=f'(0)=f'(1)=0$ and $f(1)=1$ implies $\max|f''|\geq 4$
97643
Prove that:$f(f(x)) = x^2 \implies \int_{0}^{1}{(f(x))^2dx} \geq \frac{3}{13}$
48592
Prove that $f'$ exists for all $x$ in $R$ if $f(x+y)=f(x)f(y)$ and $f'(0)$ exists
146480
Example of $\deg(fg)<\deg(f)+\deg(g)$
14952
Prove: $\frac{x}{\sqrt{y}}+\frac{y}{\sqrt{x}}\geq \sqrt{x}+\sqrt{y}$
82371
$f$ is an entire function with Im $f\geq 0$
148981
Entire $f$ and $g$ constant if $e^{f(z)}+e^{g(z)}=1$