In Exercises, find the maximum and minimum of the function f subject to the given constraint. In each case explain why the maximum and minimum must both exist.
The maximum value of the function is and the minimum value is and both exist as the constraint is a bounded and closed ellipse.
Given function is
Given constraint is
Gradients of function.
Use the method of Lagrange multipliers.
substitute in constraint.
so critical points are role="math" localid="1649893960368"
Find function value at
So the maximum value of the function is and the minimum value is
As constraint is bounded and closed ellipse so maximum and minimum both exist.
In Exercises , use the partial derivatives of and the point specified to
find the equation of the line tangent to the surface defined by the function in the direction,
find the equation of the line tangent to the surface defined by the function in the direction, and
find the equation of the plane containing the lines you found in parts and .
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