(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the set of points where the gradient of f is parallel to u =(1,1) for

f(x,y)=x^{2}+ y^{3}+ 2xy

2. Relevant equations

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

u=grad f

3. 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.

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# Gradient and parallel points of a function

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