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Find the directional derivative of \[f(x,y,z) = yz + x^4\] at (2,3,1) in the direction of vector v=i+j+k.
I have gotten as far as finding the directional derivative (gradient) at (2,3,1) which is:
32i+3j+k
I dont know how to do the second part of this problem. What does it mean to find this direction? What do I have to do to the gradient to find it? My book is very vague, please help!
 one year ago
 one year ago
Find the directional derivative of \[f(x,y,z) = yz + x^4\] at (2,3,1) in the direction of vector v=i+j+k. I have gotten as far as finding the directional derivative (gradient) at (2,3,1) which is: 32i+3j+k I dont know how to do the second part of this problem. What does it mean to find this direction? What do I have to do to the gradient to find it? My book is very vague, please help!
 one year ago
 one year ago

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xartaanBest ResponseYou've already chosen the best response.0
The box for the answer says fu= _____ , where u looks like a unit vector, is that what this is asking for? A unit vector of the gradient?
 one year ago

xartaanBest ResponseYou've already chosen the best response.0
Never mind, that, I tried, and was told my answer should be a number, not a vector. Guess I misinterpreted that.
 one year ago

UnkleRhaukusBest ResponseYou've already chosen the best response.1
\[ \newcommand \ve [1] { \mathbf{#1} }% vector \nabla_{\ve v}f(\ve x)=\nabla f(\ve x)\cdot{\ve v}\\ \ \\ f=yz+x^4\\ \ve v=(1,1,1)\]
 one year ago

xartaanBest ResponseYou've already chosen the best response.0
I think I understand what you wrote, but it still isnt clear to me what "in the direction of" means... I can find the gradient just fine, I've just no idea what to do with it.
 one year ago

UnkleRhaukusBest ResponseYou've already chosen the best response.1
once you have found the gradient, take the dot product with the direction vector
 one year ago

xartaanBest ResponseYou've already chosen the best response.0
ahhhhh, that makes sense, thank you!
 one year ago
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