Existence of $\xi$ and $\eta$ such that $f'(\xi)+f'(\eta)=\xi+\eta$
15262
Prove $\exists \xi, \eta \in (0,1)$, such that $f(\xi)+f'(\eta)=\xi+\eta$.
158520
Derivative of Fourier transform: $F[f]'=F[-ixf(x)]$
1440
Are the any non-trivial functions where $f(x)=f'(x)$ not of the form $Ae^x$
66772
$f(f(x)f(y))+f(x+y)=f(xy)$
141522
$f$ is T periodic and $f(x) + f'(x) \ge 0 \Rightarrow f(x) \ge 0$
57639
Show there exists an $\alpha\in F_{p^n}$ such that $\alpha +\alpha^p+\alpha^{p^2}+\cdots+\alpha^{p^{n-1}}\neq 0$
45682
Show that there exists a unique $v_0 \in H^1(0,1)$ such that $u(0)=\int_0^1(u'v_0'+uv_0), \forall u \in H^1(0,1)$
2717
Help proving existence of an specific $x_0$ for which $f''(x_0)=0$
75104
Existence of some type matrix
48592
Prove that $f'$ exists for all $x$ in $R$ if $f(x+y)=f(x)f(y)$ and $f'(0)$ exists
143354
Prove that there exists $c\in\mathbb{R}$ such that $f'(c)=f(c)$
90287
How to derive $[x_i, F(\vec p)] = i \hbar \frac {\partial F(\vec p)}{\partial p_i}$
24862
Solving (quadratic) equations of iterated functions, such as $f(f(x))=f(x)+x$
64339
Find $f$ where $f'(x) = f(1+x)$
112707
Must $Q^\mathsf{T}Q = I$ if $(Qx)^\mathsf{T}(Qx) = x^\mathsf{T}x$
65096
$\chi(G)+\chi(G')\leq n+1$
149399
Given continuous $f$ and $g$, there exists $c \in (a,b)$ such that $\int_{a}^{c} f(x) \ \mathrm dx = \int_{c}^{b} g(x) \ \mathrm dx$