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Use lagrange multiplier techniques to find the local extreme values of f(x, y) = x2 − y2 − 2 subject to the constraint x2 + y2 = 16
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Use lagrange multiplier techniques to find the local extreme values of f(x, y) = x2 − y2 − 2 subject to the constraint x2 + y2 = 16
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Nov 11, 2018
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Use lagrange multiplier techniques to find the local extreme values of f(x, y) = x2 − y2 − 2 subject to the constraint x2 + y2 = 16
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Given
subject to the constraint
Let
.
The gradient vectors of
and
are:
and
By Lagrange's theorem, there is a number
, such that
It can be seen that
has local extreme values at the given region.
Hamstar
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Nov 16, 2018
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