Engineering Calculus Notes 345

Engineering Calculus Notes 345 - values of f x,y,z = 2 x 2...

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3.6. EXTREMA 333 and an even number of the variables can be negative. This yields four relative critical points, at all of which f ( x,y,z ) = 3: (1 , 1 , 1) , (1 , 1 , 1) , ( 1 , 1 , 1) , ( 1 , 1 , 1) . To see that they are the closest (not the furthest) from the origin, simply note that there are points on this surface arbitrarily far from the origin, so the distance to the origin is not bounded above. Finally, let us consider a “full” optimization problem: to ±nd the extreme
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Unformatted text preview: values of f ( x,y,z ) = 2 x 2 + y 2 − z 2 inside the unit ball x 2 + y 2 + z 2 ≤ 1 (see Figure 3.27 ). • f ( x,y,z ) = 0 • f ( x,y,z ) = 2 • f ( x,y,z ) = 1 • f ( x,y,z ) = − 1 x y z Figure 3.27: Critical Points of f ( x,y ) = 2 x 2 + y 2 − z 2 inside the Ball x 2 + y 2 + z 2 ≤ 1...
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