Question

Let \[f(x,y): z=xy ^{2}\] be a surface in \[R ^{3}\]
Let the constraint be \[g(x,y): x+4y=4\]
Apply the method of lagrange and interpret the results.

Answer 1

Take gradient of f and g

Answer 2

\[\nabla F=\lambda \nabla G \]

Answer 3

Is z= in the first equation redundant?

Answer 4

since f(x,y) is there