query: Find the maximum of $f(x) =\int_0^x\sqrt{(x^2-x)^2+y^4}\, dy, x\in[0,1].$
positive_passages.docid: 154223
positive_passages.text: Find the maximum value of $ f(x) = \int^{x}_{0} \sqrt{(x^2-x)^2+y^4}~dy$
negative_passages.docid: 87513
negative_passages.text: Global maximum and minimum of $f(x,y,z)=xyz$ with the constraint $x^2+2y^2+3z^2=6$ with Lagrange multipliers?
negative_passages.docid: 26754
negative_passages.text: Find all continuous functions satisfying $\int_0^xf=(f(x))^2+C$ for some constant $C \neq 0$.
negative_passages.docid: 104145
negative_passages.text: Finding the value of $3(\alpha-\beta)^2$ if $\int_0^2 f(x)dx=f(\alpha) +f(\beta)$ for all $f$
negative_passages.docid: 127634
negative_passages.text: query on maximum minimum of multi-variable function
negative_passages.docid: 153798
negative_passages.text: Problem involving maximum and minimum of a continuous function
negative_passages.docid: 19631
negative_passages.text: Finding $\lim_{n\to \infty}\sqrt n \int_0^1 \frac{\,dx}{(1+x^2)^n}$
negative_passages.docid: 53748
negative_passages.text: Find maximum value of $\int_{0}^{1}\left(f(x)\right)^3dx$
negative_passages.docid: 136655
negative_passages.text: Find the range of the given function $f$
negative_passages.docid: 133851
negative_passages.text: How to arrive at $\int_{0}^{1} f^3(x) \, dx < (\int_{0}^{1} f(x) \, dx)^2$?
negative_passages.docid: 98255
negative_passages.text: Find $f(x)$ such that $f(f(x)) = x^2 - 2$
negative_passages.docid: 39451
negative_passages.text: Proving inequation with maximum and 2nd derivative
negative_passages.docid: 98344
negative_passages.text: Prove that $\int_0^1[f''(x)]^2dx\ge4.$
negative_passages.docid: 99930
negative_passages.text: Find the Maximum value of $\frac{x}{\sqrt{x+y}}+\frac{y}{\sqrt{y+z}}+\frac{z}{\sqrt{z+x}}$
negative_passages.docid: 148470
negative_passages.text: bound of the function
negative_passages.docid: 46883
negative_passages.text: Demand $z=x+y$ and $x^2/4 + y^2/5 + z^2/25 = 1$. What is the maximum value of $f(x,y,z) = x^2+y^2+z^2$?
negative_passages.docid: 54797
negative_passages.text: Find the continuous function defined over $[0,1]$ such that $\int_0^1f(x){\rm d}x=1, \int_0^1 xf(x){\rm d}x=a$ and $\int_0^1x^2f(x){\rm d}x=a^2 .$