The function f(x, y,z)equals2 x plus z squared has an absolute maximum value and absolute minimum value subject to the constraint x squared plus 2 y squared plus 3 z squaredequals16. Use Lagrange multipliers to find these values.

Absolute maxima an minma both occured at .

Step-by-step explanation:

Given function is,

subject to,

Let

To find absolute maxima and absolute minima using Lagranges multipliers method consider as the multipliers such that,

on compairing both side we get,

From (2),

Absolute maxima, at x=3, y=0, is,

Absolute minima, at x=3, y=0, is,

Hence the result.

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18. g

20. h 30 degree turn.

21. d 90 degree angles

and also 19 is a. a sphere not a cirlcle

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step-by-step explanation: