Find Minimum and Maximum Values of Functions: Problems with Solutions

By Denitsa Dimitrova (Bulgaria)
Problem 1
Find the minimum and maximum values of the function
$f(x)=x^4-2x^2+5$ on $[-3,3]$
Problem 2
Find the minimum and maximum values of the function
$f(x)=x^4-2x^2+5$ on $[-1,1]$
Problem 3
Find the minimum and maximum values of the function
$f(x)=(x-2)^3$ on $[0,2]$
Problem 4
Find the minimum and maximum values of the function
$f(x)=(1-x)^3$ on $[-1, 1]$
Problem 5
Find the minimum and maximum values of the function
$f(x)=-x^2-x+2$ on $[-1,2]$
Problem 6
Find the minimum and maximum values of the function
$f(x)=x^4-8x^2-9$ on $x\in[0,3]$
Problem 7
Find the minimum value of the function
$f(x)=2|x-3|+x^2$ on $[5, 7]$
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