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allsmiles

  • 3 years ago

Give the unit vector that has the direction of maximum increase of the function . f(x, y) at the location (−2, 1). For f(x,y)=x^2+2y^2-y

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  1. surdawi
    • 3 years ago
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    plug in x and y

  2. surdawi
    • 3 years ago
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    f(-2,1)=(-2)^2+2*1^2-1

  3. TuringTest
    • 3 years ago
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    you will need the gradient first I think

  4. allsmiles
    • 3 years ago
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    Yeah is the answer not the gradient divided by the mag?

  5. allsmiles
    • 3 years ago
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    to get the unit vector? Since the max increase is in the same direction as the gradient?

  6. TuringTest
    • 3 years ago
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    yes, it should be gradient divided by magnitude

  7. TuringTest
    • 3 years ago
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    well, the gradient is the maximum direction of change; could be increase or decrease

  8. allsmiles
    • 3 years ago
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    so how do you know if it's increase or decrease?

  9. TuringTest
    • 3 years ago
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    I'm actually not too sure in this case. You could do it with multivariable max/min techniques if you know them.

  10. allsmiles
    • 3 years ago
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    alright man thanks for your help much appreciated

  11. TuringTest
    • 3 years ago
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    welcome

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