Prove that if $f'(x)=f(x)$ for all $x$, then there exist a constant $c$ such that $f(x)=ce^x$ for all $x$
10431
Prove that $C\exp(x)$ is the only set of functions for which $f(x) = f'(x)$
158647
If $|f(z)|\le |f(z^2)|$ then prove that $f$ is constant
75390
How does one prove that if function's partial derivative respect to every variable is zero, function is constant?
34223
Prove that every function that verifies $|f(x)-f(y)|\leq(x-y)^2$ for all $x,y$ is constant.
90199
Prove that there exists a constant $c>0$ such that the following happens
149586
If $\lim_{x\to\infty} f'(x) = L$, prove that $\lim_{x\to\infty} f(x+c)-f(x) = cL$ and $\lim_{x\to\infty} f(x)/x=L$
132113
Does $f(x) = f(2x)$ for all real $x$, imply that $f(x)$ is a constant function?
55492
Existence of $f'\in F$ such that $f^{[G:F]}=(f')^n$ for finite extension $F\subset G$
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).
32506
Prove $kf(x)+f'(x)=0 $ when conditions of Rolle's theorem are satisfied .
111186
Proving that if $|f''(x)| \le A$ then $|f'(x)| \le A/2$
74583
Prove that $f'(0)=L$.
8179
If $f$ is entire and $|f|\geq 1$, then show $f$ is constant.
61640
Prove c exists for f:[0,1] -> R
105700
Proving $\,f$ is constant.
139111
Prove that $a<c<b$, $\frac{f(b)-f(a)-(b-a)f'(a)}{g(b)-g(a)-(b-a)g'(a)}=\frac{f"(c)}{g"(c)}$
72856
Show $f$ is constant if $|f(x)-f(y)|\leq (x-y)^2$.