Find all derivable functions such that $f(0)=0$ and $|f'(x)|≤|f(x)|,∀x∈\mathbb{R}$
33247
Does $f(0)=0$ and $\left|f^\prime(x)\right|\leq\left|f(x)\right|$ imply $f(x)=0$?
75390
How does one prove that if function's partial derivative respect to every variable is zero, function is constant?
35889
Suppose that f(0) = f(1) = 0 and x ∈ (0, 1). Prove that there exists c ∈ (0, 1) such that f'(c) = f(x).
11453
Find a real function $f:\mathbb{R}\to\mathbb{R}$ such that $f(f(x)) = -x$?
30855
Finding all differentiable $f(z) = u(x) + iv(y)$ in $\mathbb{C}$ where $u(x),v(y)$ are real valued functions.
99917
What function satisfies $F'(x) = F(2x)$?
1440
Are the any non-trivial functions where $f(x)=f'(x)$ not of the form $Ae^x$
25467
Prove that $\lim f(x) =0$ and $\lim (f(2x)-f(x))/x =0$ imply $\lim f(x)/x =0$
40070
Is there a real-valued function $f$ such that $f(f(x)) = -x$?
17310
Can $f(x)=|x|^3$ be differentiated
10431
Prove that $C\exp(x)$ is the only set of functions for which $f(x) = f'(x)$
113888
Behavior of derivative near the zero of a function.
39090
Finding functions such that $f(g(x)) = f(x)g(x)$
13202
Prove that there exists at least one $x_0\in\mathbb{R}$, such that $f(x_0)+f''(x_0)=0$
73519
Determine all functions satisfying $f(x + f(x + y)) + f(xy) = x + f(x + y) +yf(x)$
28286
About finding the function such that $f(xy)=f(x)f(y)-f(x+y)+1$
150502
If $f(0) = 0$ and $|f'(x)|\leq |f(x)|$ for all $x\in\mathbb{R}$ then $f\equiv 0$