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Using Lagrange multipliers to find minimum values

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MA312 - CALCULUS-2 (GRANTHAM UNIVERSITY) WEEK-5 - Would like to get the detailed answers to all questions.

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We solve various problems in multivariable calculus.

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Minimum Value, Maximum Value, and Saddle Points

1) Find the local maximum and minimum values and saddle point(s). Here is the function:

f(x,y) = x^3y + 12x^2 -8y

2) Use Lagrange multiplier to find the extreme values (i.e. the max and min) of:

f(x,y) = 4x+6y

subjected to the constraint

x^2 + y^2 = 13

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