Difficult

Extremal value problems: Very Difficult Problems with Solutions

Problem 1
Find the value of the positive real parameter a, for which the minimal value of the function [tex]f(x)=(a^2+1)x^2-2ax+10[/tex] in the interval [tex]x \in [0; \frac{1}{2}][/tex] is [tex]f_{min}(x)=\frac{451}{50}[/tex]
Difficult
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