Minimize $\int\limits _{0}^{1} f^2(x) dx$ if $\int\limits_{0}^{1} f(x) dx = 1$, $\int\limits_{0}^{1} xf(x)dx = 1$
33389
What's the minimum of $\int_0^1 f(x)^2 \: dx$, subject to $\int_0^1 f(x) \: dx = 0, \int_0^1 x f(x) \: dx = 1$?
21065
Bordered Hessian matrix to find a minimum of the function
78008
A conjectured closed form of $\int\limits_0^\infty\frac{x-1}{\sqrt{2^x-1}\ \ln\left(2^x-1\right)}dx$
38702
How to minimize $|z_1 - z_2|^2 + |z_1 - z_4|^2 + |z_2 - z_3|^2 + |z_3 - z_4|^2$?
126259
Minimum of a function on an open interval
155415
Minimax problem for optimization $\inf \sup \frac{x f(x)}{\int_0^1 f(t) dt}$
143874
Limit of derivative is zero. Does it imply a limit for f(x)?
37337
Minimizing a functional with a free boundary condition
77983
Shortest method for $\int_{0}^{1}\frac{x^{4}\left(1-x\right)^{4}}{1+x^{2}}$
39179
Why is $(0, 0)$ not a minimum of $f(x, y) = (y-3x^2)(y-x^2)$?
93806
$\|f\|_{L^{p}}=\sup\left\{\int_{{\bf R}^{n}}|f(x)g(x)|~dx:\|g\|_{L^{q}}\le1\right\}$
3885
Maximum and minimum of of $f(x)=|x-1|+|x-2|+|x-3|$
144146
find a $\int_{x}^{g(x)} f(t)\,dt = 1$
153267
Proving $\lim\limits_{x \to \infty} xf(x)=0$ if $\int_{0}^{\infty}f(x) dx$ converges.
83479
Example how maximizing and minimizing a function can be equivalent?
87513
Global maximum and minimum of $f(x,y,z)=xyz$ with the constraint $x^2+2y^2+3z^2=6$ with Lagrange multipliers?
44653
$(\int f_1d\mu)^2+\cdots+(\int f_nd\mu)^2\leq(\int \sqrt{f_1^2+\cdots+f_n^2}d\mu)^2$