Prove\disprove: Let $F : \Bbb{R}^2\to \Bbb{R}$ a function s.t $\nabla F(x,y)=(0,0)$ for all $(x,y)$, so $F$ is constant.
114826
Zero Partials imply Constant Function Theorem or Proof
73547
Prove that is $\bar{f}g$ is analytic then $f$ is constant or...?
77331
$f$ function with $\nabla f=\bar{0}$
48592
Prove that $f'$ exists for all $x$ in $R$ if $f(x+y)=f(x)f(y)$ and $f'(0)$ exists
56127
Prove a function is constant under certain conditions
87743
Is a function whose derivative vanishes at rationals constant?
10727
Let $f$ be an entire function and $L$ a line in $\mathbb{C}$ such that $f(\mathbb{C})\cap L=\emptyset$. Show that $f$ is constant function.
8854
Prove $f $ is identically zero if $f(0)=0$ and $|f'(x)|\le|f(x)|$
113343
$f$ is constant if derivative equals zero
154034
Suppose that $f(x)$ is continuous on $(0, \infty)$ such that for all $x > 0$,$f(x^2) = f(x)$. Prove that $f$ is a constant function.
7878
Proving that a doubly-periodic entire function $f$ is constant.
15032
Let $f: \Bbb R \to \Bbb R$ be a differentiable function such that $\sup_{x \in \Bbb R}|f'(x)| \lt \infty$. Then
96539
is $f$ constant or dilation
155864
Prove or disprove: if $y'=y-y^2$ and $y(0)=a$ where $00$
158647
If $|f(z)|\le |f(z^2)|$ then prove that $f$ is constant
9451
Show bounded and convex function on $\mathbb R$ is constant
121771
Proof $f(x)\equiv 0$