Completing The Square Generalized
For real numbers \(x\), \(y\) and \(z\), function \[f(x,y,z)=4x-x^2-y^2-z^2+18\] has a maximum value \(d\) at \(x=a\), \(y=b\) and \(z=c\). What is the value of \(a+b+c+d\)?
For real numbers \(x\), \(y\) and \(z\), function \[f(x,y,z)=x^2+y^2+z^2-4x-4y-4z+14\] has a minimum value \(d\) at \(x=a\), \(y=b\) and \(z=c\). What is the value of \(a+b+c+d\)?
For real numbers \(x\) and \(y\), function \[f(x,y)=x^2+2y^2-4x-16y+21\] has a minimum value \(c\) at \(x=a\) and \(y=b\). What is the value of \(a+b-c\)?
For real numbers \(x\) and \(y\), function \[f(x,y)=2x-x^2+2y-y^2+28\] has a maximum value \(c\) at \(x=a\) and \(y=b\). What is the value of \(a+b+c\)?
What is the maximum value of \(f(f(x))\) in the domain \(2 \leq x \leq 5\) for the function \[f(x)=x^2-6x+4?\]