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Math Help - Average and instantaneous rate of change of f.

  1. #1
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    Average and instantaneous rate of change of f.

    Another one I'm currently stuck on:

    "Let f(x,y)=x^2+ln(y). Find the average rate of change of f as you go from (3,1) to (1,2). Find the instantaneous rate of change of f as you leave the point (3,1) heading toward (1,2)."

    What exactly am I supposed to do in order to solve this problem?
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  2. #2
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    I believe the average rate of change is given by:

    \dfrac{f(1,2) - f(3,1)}{\sqrt{(1-3)^2 + (2-1)^2}}

    I believe the instantaneous rate of change is given by the directional derivative. If \mathbf u = <1-3,2-1> = <-2,1> = <u_1,u_2>, then the directional derivative is given by:

    \mathbf{D_u}f(3,1) = f_x(3,1)u_1 + f_y(3,1)u_2 = f_x(3,1)(-2) + f_y(3,1)(1) = -12 + 10 = -2
    Last edited by NOX Andrew; February 28th 2011 at 05:59 PM.
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