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xartaan

  • 3 years 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!

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  1. xartaan
    • 3 years ago
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    Tips?

  2. xartaan
    • 3 years ago
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    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?

  3. xartaan
    • 3 years ago
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    Never mind, that, I tried, and was told my answer should be a number, not a vector. Guess I misinterpreted that.

  4. xartaan
    • 3 years ago
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  5. UnkleRhaukus
    • 3 years ago
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    \[ \newcommand \ve [1] { \mathbf{#1} }% vector \nabla_{\ve v}f(\ve x)=\nabla f(\ve x)\cdot{\ve v}\\ \ \\ f=yz+x^4\\ \ve v=(1,1,1)\]

  6. xartaan
    • 3 years ago
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    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.

  7. UnkleRhaukus
    • 3 years ago
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    once you have found the gradient, take the dot product with the direction vector

  8. xartaan
    • 3 years ago
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    ahhhhh, that makes sense, thank you!

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