I'm Given The Equation F(x,y) = -4x3 + 4xy - 2y2...

MythBrainy

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I'm given the equation f(x,y) = -4x3 + 4xy - 2y2 +1. point p = (2,1) The question is: Find the slope of f at the given point p inthe direction (3,4)

 

Answer No.1

TheGreatGuy

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The gradient of f is (-12x^2+4y)i + (4x - 4y)j The gradient of f at (2,1) is -44i + 4j. A vector from (2,1) to (3,4) is i + 3j. Normalizing the vector, we get (1/√10)(i+3j) The slope is the gradient dot above vector = (1/√10)(-44(1) +4(3)) = you can simplfiy.

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