Algebra

Completing The Square Generalized

Completing the Square - Multiple Variables

         

For real numbers xx, yy and zz, function f(x,y,z)=4xx2y2z2+18f(x,y,z)=4x-x^2-y^2-z^2+18 has a maximum value dd at x=ax=a, y=by=b and z=cz=c. What is the value of a+b+c+da+b+c+d?

For real numbers xx, yy and zz, function f(x,y,z)=x2+y2+z24x4y4z+14f(x,y,z)=x^2+y^2+z^2-4x-4y-4z+14 has a minimum value dd at x=ax=a, y=by=b and z=cz=c. What is the value of a+b+c+da+b+c+d?

For real numbers xx and yy, function f(x,y)=x2+2y24x16y+21f(x,y)=x^2+2y^2-4x-16y+21 has a minimum value cc at x=ax=a and y=by=b. What is the value of a+bca+b-c?

For real numbers xx and yy, function f(x,y)=2xx2+2yy2+28f(x,y)=2x-x^2+2y-y^2+28 has a maximum value cc at x=ax=a and y=by=b. What is the value of a+b+ca+b+c?

What is the maximum value of f(f(x))f(f(x)) in the domain 2x52 \leq x \leq 5 for the function f(x)=x26x+4?f(x)=x^2-6x+4?

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