Math222Assignment 6due Wednesday Nov. 7, 20071. The functionz=Z(x, y) is defined implicitly by the equationx2+y2+ 4z2+z4= 64(a) Find∂z∂x,∂z∂y,∂2z∂x2, and then evaluate these at the pointP=(4,4,2).(b) Find the equation of the tangent plane to the surface defined aboveat the pointP.(c) Find∇ZatPand find the direction of maximum increase of thefunctionZ.2. Find the critical points indicating (with your justification) which are localmaxima, local minima, and which are saddle points of the function.z=xy e-(x2+4y2)/23. Letzbe defined implicitly byz3+ 4z= 2x2y+ 12.Takingxandyas independent variables, find all the first and second partials ofzandevaluate these at (x, y) = (1,2) given that
This is the end of the preview.
access the rest of the document.