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anonymous
 5 years ago
how do i find the unit vector in the direction for which the directional derivative of f at the point (3,4) is maximum? f(x,y)=x^2+6y^2
anonymous
 5 years ago
how do i find the unit vector in the direction for which the directional derivative of f at the point (3,4) is maximum? f(x,y)=x^2+6y^2

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i found the gradient of f(x,y) already, but then what?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Is that exactly how the question is phrased? I'm a bit perplexed by the maximum part.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yes, but i got the answer already. it is the same gradient vector of f.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Ok, good, makes sense :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Do u know how to do this btw? Find the unit vector in the direction for which the directional derivative of f at the point (3,4) is zero. \[f(x,y)=x ^{2}+6y ^{2}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0NIGHTIE I M BACK CM ON CHAT BOX

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Unit vector = U Gradient vector = G (U/U)*G=0 Solve U as 8i+j for example, use DOT product between the vectors obviously. :) Anywhere you want me to explain more?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0please explain more, i got the dot product part but then wouldn't G equal to 0 at the end?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0That's the point, you are given that the directional derivative at point (3,4) is 0. The formula for computing the directional derivative is unit vector * G vector. So all you really need to do is match the unit vector so the dot product equals the directional derivative which is 0 in this case.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Do I make sense for you? :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so the answer would be <0,0>?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0wouldnt it just be enough to find the gradient at 3,4 and then find the unit vector?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0You have this: G = 2xi + 12yj G(3,4) = 6i + 48j You're now looking for a unit vector that would satisfy the equation of: U*G = 0 Basically you want the dot product between those two vectors to equal 0. A 0i +0j vector is not a unit vector. So you want to rephrase the equation like this instead: Unit vector = vector / vector S for example the dot product between 8i+j * 6i +48j = 0 But 8i + j / 8i +j is still a unit vector, so nothing wrong there. Answer would then be 8i + j / 8i +j = (8i + j) / sqrt(65)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Yes Him, that's what I said.. ;)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0bt then that would be (6i+48j)/sqrt (2340) wont it?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Ah, I missunderstood your question, no that would make the gradient vector a unit vector, and that's not the same thing.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so is what im saying wrong?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I dont actually know this. I'm not sure what happens if you convert the gradient to a unit vector, but then you'd still have to find the unit vector U so it matches unit of the gradient and still equals 0 in the dot product. Imo it would make things more complicated then they should be.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0nd i dont understand how the directional derivative can be MAXIMUM or MINIMUM. From what i know , its just the unit vector of the gradient of a field at a given point, isnt it? Even i dunno vector calc much...

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Good Nikie :) Glad to help!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yeah...thanx...this makes me understand

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0NIGHTIE BHAIYA I HAD TOLD U SOLUTION ITS MY GREAT PLEASURE

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0mera fan banne ke liye DHANYAVAD
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