Each of these extreme value problems has a solution with both a maximum value and a minimum value. Use Lagrange multipliers to find the extreme values of the function subject to the given constraint. f(x,y)=X^2-y^2;x^2+y^2=1
Each of these extreme value problems has a solution with both a maximum value and a minimum value. Use Lagrange multipliers to find the extreme values of the function subject to the given constraint. f(x,y)=X^2-y^2;x^2+y^2=1
Lagrange's method of multipliers
For a function of two or more variables this method is used.
Let f(x, y)=0 be the function within the condition h(x, y)=0.
First evaluate partial derivative of function and the constraint with respect to x and y and then obtain Lagrange's equation
Evaluate x and y in terms of k and substitute these values in the given condition to obtain k and then x and y which do not have k in their value.
Put value of x and y in the function to obtain minimum or maximum.
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