Directional derivative

  • Thread starter Master J
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  • #1
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I have a function of 2 variables. I know it increase most rapidly in the direction of the gradient, but how about in wht direction is it not increasing?

I am thinking that the gradient (dot product)(direction in which it is not increasing) = 0

Any hints?
 

Answers and Replies

  • #2
CompuChip
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Well, since you mentioned the word "directional derivative" anyway: you could check for which [itex]\vec v[/itex]
[tex](\vec\nabla f(x, y)) \cdot \vec v < 0[/tex]
?
 
  • #3
HallsofIvy
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Yes, it is true that [itex]\vector{\nabla f}\cdot \vector v[/itex] is the directional derivative in the directional derivative in the direction of [itex]\vec{v}[/itex] (for [itex]\vec{v}[/itex] of length 1). And that tells you the derivative is 0 perpendicular to the gradient.

(CompuChip, surely you didn't mean "<"?)
 
  • #4
CompuChip
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Err, no comment? :)
 
  • #5
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That is what is was thinking, since of course cos(pi/2) = 0. So the vector that is at a right angle to the gradient is in the direction of zero increase. But how do I go about finding this vector?
 

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