The discussion focuses on finding two unit vectors for the function f(x,y) = x² - xy + y² such that the directional derivative D_vf equals zero. The gradient of the function, ∇f, is essential in determining the required unit vectors, which must be perpendicular to ∇f. The previously calculated unit vector u = (1/√2)(i + j) is not relevant for this specific task, as the problem requires identifying vectors v that satisfy the condition D_vf = 0.
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This problem doesn't have anything to do with the vector "u". Why is that given? D_vf is the dot product of the gradient, \nabla f, and a unit vector in the same direction as vector v. Since you want that to be 0, you are looking for two unit vectors perpendicular to \nabla f.Cpt Qwark said:Homework Statement
For f(x,y)=x^2-xy+y^2 and the vector u=i+j.
ii)Find two unit vectors such D_vf=0
2. Homework Equations
So "u" was used in previous questions?N/A.
The Attempt at a Solution
Not sure if relevant but the previous questions were asking for the unit vector u - which I got \hat{u}=\frac{1}{\sqrt{2}}(i+j) for the maximum value of D_uf which was \sqrt{2}.