Extremal value problems: Difficult Problems with Solutions

Problem 1
Find the maximal value of the function [tex]f(x)=-x^2+18x+3[/tex].
Problem 2
Find the maximal value for the function [tex]f(x)=\sqrt{2}|sinx+cosx|[/tex].
Problem 3
Find the minimal value of the function [tex]f(x)=|1+|x-1||[/tex].
Problem 4
Find the minimal value of the function [tex]f(x)=x^2+5x+1[/tex].
Problem 5
Find the minimal value of the function [tex]f(x)=x^2+8x+15[/tex].
Problem 6
Find the value of x, for which the function [tex]f(x)=-x^2-10x+8[/tex] has maximal value.
Problem 7
Find the minimal value of [tex]f(x)=\frac{1}{4}x^4+x^3+2x^2-8x+15[/tex].
Problem 8
Find the minimal value of the function [tex]f(x)=\frac{1}{4}x^4-2x^3+\frac{11}{2}x^2-6x+8[/tex].
Problem 9
Find the maximal value of the function [tex]f(x)=cos^2x+2cosx+2sin^2x[/tex].
Problem 10
Find the minimal value for the function [tex]f(x)=log_2(|x|+2)[/tex]

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