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 \(a+b+c+d\)?

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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 \(a+b+c+d\)?

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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 \(a+b-c\)?

Excel in math and science

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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 \(a+b+c\)?

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, conceptual quizzes.

Our wiki is made for math and science

Master advanced concepts through explanations,
examples, and problems from the community.

Used and loved by 4 million people

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including olympiad champions, researchers, and professionals.

Your answer seems reasonable.
Find out if you're right!