Use Lagrange multipliers to find the maximum and minimum values. f(x,y)=(x^2)y,x^2+y^2=4
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Use Lagrange multipliers to find the maximum and minimum values.
f(x,y)=(x^2)y,x^2+y^2=4
Consider the given function and the constraint .
Note that, .
That implies,
From (1),
From (2),
That implies,
Substitute in .
Substitute in .
Substitute in .
Step by step
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- Use Lagrange multipliers to find the minimum distance from the curve or surface Line: x − y = 4 to the point (0, 2).Use Lagrange multipliers to find the point (a,b) on the graphof y = e4x, where the value ab is as small as possible.P =Use Lagrange multipliers to find the minimum distance from the curve or surface to the indicated point.Curve - Line: x − y = 2 Point- (0, 2)