query: If $Df(c)=0$ $\forall c\in V$ then $f$ is constant on $V$
positive_passages.docid: 23615
positive_passages.text: Why does zero derivative imply a function is locally constant?
negative_passages.docid: 137043
negative_passages.text: To show that function is constant
negative_passages.docid: 147516
negative_passages.text: Continuous function whose right hand derivative equals 0 is constant?
negative_passages.docid: 42075
negative_passages.text: If $f$ is analytic then $|f|$ is not constant unless $f$ is constant
negative_passages.docid: 64650
negative_passages.text: If $a\operatorname{Re}(f(z))+b\operatorname{Im}(f(z))=c$ then f is constant
negative_passages.docid: 114488
negative_passages.text: If $|f|+|g|$ is constant on $D,$ prove that holomorphic functions $f,~g$ are constant on $D$.
negative_passages.docid: 104510
negative_passages.text: For continuous $f$, $\int_0^x f(t)dt = ∫_x^1f(t)dt$ implies $f=0$.
negative_passages.docid: 51934
negative_passages.text: Let $f$ be entire and suppose that $\text{Im} f\ge0$. Show that $\text{Im} f$ is constant.
negative_passages.docid: 114179
negative_passages.text: If $Var(X)=0$ then is $X$ a constant?
negative_passages.docid: 75390
negative_passages.text: How does one prove that if function's partial derivative respect to every variable is zero, function is constant?
negative_passages.docid: 73547
negative_passages.text: Prove that is $\bar{f}g$ is analytic then $f$ is constant or...?
negative_passages.docid: 90199
negative_passages.text: Prove that there exists a constant $c>0$ such that the following happens
negative_passages.docid: 141863
negative_passages.text: If the imaginary part of an entire function is never zero, the function is constant
negative_passages.docid: 727
negative_passages.text: Prove that any continuous integer-valued function of a real variable is constant.
negative_passages.docid: 63845
negative_passages.text: Diffeomorphism $f:U\to V$ then $Df:\mathbb{R^n}\to\mathbb{R^m}$ will be linear isomorphism hence $n=m$
negative_passages.docid: 154742
negative_passages.text: If $f(z)$ analytic in the domain $D$ and $f'(z)=0$ so $f(z)=$constant?
negative_passages.docid: 13765
negative_passages.text: Is a rational-valued continuous function $f\colon[0,1]\to\mathbb{R}$ constant?