Gradient and parallel points of a function

[wolfgangjt]

Homework Statement

Find the set of points where the gradient of f is parallel to u =(1,1) for
f(x,y)=x² + y³ + 2xy

Homework Equations

the gradient of f(x,y)=((partial derivative of f wrt x), (partial derivative of f wrt y))
u=grad f

The Attempt at a Solution

f_x = 2x+2y
f_y = 3y+2x

1=2x+2y
1=3y+2x

x=1/2
y=0

I set the partials equal to the respective values of u and solved and got one set of points. I have a feeling this is wrong. I got x= 1/2 and y= 0

I looked through the notes and cannot find anything to help me with this so I came here in hope of getting pointed in the right direction.

 

[SammyS]

You don't need grad(f) = u, they're just parallel, so grad(f) = c*u, for any scalar c.