anonymous
  • anonymous
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
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
plug in x and y
anonymous
  • anonymous
f(-2,1)=(-2)^2+2*1^2-1
TuringTest
  • TuringTest
you will need the gradient first I think

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anonymous
  • anonymous
Yeah is the answer not the gradient divided by the mag?
anonymous
  • anonymous
to get the unit vector? Since the max increase is in the same direction as the gradient?
TuringTest
  • TuringTest
yes, it should be gradient divided by magnitude
TuringTest
  • TuringTest
well, the gradient is the maximum direction of change; could be increase or decrease
anonymous
  • anonymous
so how do you know if it's increase or decrease?
TuringTest
  • TuringTest
I'm actually not too sure in this case. You could do it with multivariable max/min techniques if you know them.
anonymous
  • anonymous
alright man thanks for your help much appreciated
TuringTest
  • TuringTest
welcome

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