Note that the domain of definition of f (x, y) is the closed unit disk x^2 + y^2≤1. a) Find and classify all critical points inside x^2 + y^2 <1 as relative maximum, relative minimum, or saddle point. Use the Gundelfinger criterion with the Hessians (that is, the criterion of the second derivative). b) Find the extremes of f at the boundary x^2 + y^2 = 1. c) Determine the absolute maxima and minima of f.
1) Let (see img 1)
Note that the domain of definition of f (x, y) is the closed unit disk x^2 + y^2≤1.
a) Find and classify all critical points inside x^2 + y^2 <1 as
b) Find the extremes of f at the boundary x^2 + y^2 = 1.
c) Determine the absolute
2) Use the Lagrange multipliers to find the smallest distance between the plane 2x + 3y + 6z = 98, and the ellipsoid (x^2/9) + y^2 + 9z^2 = 1.
Hint: you can use the formula that says that the distance between such a plane and a point (x0, y0, z0) of the ellipsoid is equal to the absolute value of the quotient (see img 2)
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