If $E\subset \mathbb{R}$, $f:E\to\mathbb{R}^m$, and $||f(x)||=1$ for all $x\in E$, then $f'(x)\cdot f(x)=0$ for all $x$
123911
Why is the derivative of a vector orthogonal to the vector itself?
121771
Proof $f(x)\equiv 0$
138544
For which values of $x$, will $f (x) . f '(x) < 0$?
66404
Prove that:$\int_{a}^{b} f(x) dx = b \cdot f(b) - a \cdot f(a) - \int_{f(a)}^{f(b)} f^{-1}(x) dx$
156235
Are $x \cdot 0 = 0$, $x \cdot 1 = x$, and $-(-x) = x$ axioms?
100765
If $f'(x) = 0$ for all $x \in \mathbb{Q}$, is $f$ constant?
69008
$f'(x) = [f(x)]^{2}$. Prove $f(x) = 0 $
88690
$\int_a^b f(x)\mathrm dx=0$ for all $-\infty<a<b<\infty$ a,b rational implies $f=0$ a.e
84510
If $f(\mathbb{C})\subset \mathbb{C}-[0,1]$ then $f$ is constant
84313
$|f(z)|\le 1-|z|\forall z\in D$, we need to show $f\equiv 0$
134043
Prove that for $ f(x+2\cdot\pi)=f(x), x \in \mathbb{R} $, there exists $ x_0 $ so $ f(x_0+\pi)=f(x_0) $
104510
For continuous $f$, $\int_0^x f(t)dt = ∫_x^1f(t)dt$ implies $f=0$.
44761
Is $f'(x)-3f(x) = 0$ subspace of differentiable functions $f\colon (0,1)\to \mathbb{R}$
81181
Prove that $\det(M-I)=0$ if $\det(M)=1$ and $MM^T=I$
82371
$f$ is an entire function with Im $f\geq 0$
111515
Proving that $-a=(-1)\cdot a$
72847
Does $f(x)$ is continuous and $f = 0$ a.e. imply $f=0$ everywhere?