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Hi, my teacher gave us this problem, and he couldn't figure out why

method was incorrect and why I got the answer I did.

Given we know the gradient slope = <-56,1.886> at the point (2,0) on a

surface f(x,y), in what direction, expressed as a unit vector, is f

increasing most rapidly?

[Difficulty]

I solved the problem like this:

Max slope = magnitude of gradient slope

(gradient slope) dot (unit vector) = 56.03

-56.03Ux + 1.866Uy = 56.03

sqt(Ux^2 + Uy^2) = 1

Solving the system Ux= -.9977 Uy=.0672

The only problem is, by definition, I should be able to get the unit

vector by taking the gradient slope vector and dividing by the

magnitude of the gradient vector. or,

<-56/56.03, 1.886/56.03> = <Ux,Uy> = <-.9994,.0336>

The weird thing is, the correct Uy value is almost exactly half of

mine...what's going on???

[Thoughts]

I tried a similiar technique for finding where the ∇f = 0

<-56, 1.866> dot (unit vector) = 0

-56.03Ux + 1.886Uy = 0

sqt(Ux^2 + Uy^2) = 1

Solving the system this time I got the correct answer, why here and

not there?

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