Finding Points of Parallel Tangent Plane for z=(x^2)(e^y)

[nirali35]

Homework Statement

Find the points on the graph of z=(x^2)(e^y) at which the tangent plane is parallel to 5x-2y-.5z=0

Homework Equations

An equation of the tangent plane to z=f(x,y) at (a,b) is:
z = f(a,b) + fx(a,b)(x-a) + fy(a,b)(y-b)

The Attempt at a Solution

Partial derivatives of function f(x,y)
fx(x,y) = 2xe^y => fx(a,b) = 2ae^b
fy(x,y) = (x^2)(e^y) => fy(a,b) = (a^2)(e^b)

 

[lanedance]

ideas from here? you could check when the plane normal vectors are parallel, or alternatively check when the directions of both the partial derivatives are perpindicular to the plane normal

you can also do this with graidents, but it amounts to a similar thing