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Math Help - An Approximation to a partial Derivative

  1. #1
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    An Approximation to a partial Derivative

    An Approximation to a partial Derivative

    If a function is known to have
    fx(30,24) = -.4
    fy(30,24) = 1.2
    f(30,24) = 50

    Estimate this value of F.
    f(30.2,23.9)


    Thank you for helping me. I am stuck on the last part
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  2. #2
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    Quote Originally Posted by Applestar13 View Post
    An Approximation to a partial Derivative

    If a function is known to have
    fx(30,24) = -.4
    fy(30,24) = 1.2
    f(30,24) = 50

    Estimate this value of F.
    f(30.2,23.9)

    Thank you in advance! I am stuck on this part. Both s and y changed and have no idea what to do.
    the idea of approximating a two variable function around a given point is to use the tangent plane (at the given point) to the surface that the function represents as

    the approximation, i.e. f(x,y) \approx f(x_0,y_0)+(x-x_0)f_x(x_0,y_0)+(y-y_0)f_y(x_0,y_0). so if we put x=30.2, \ y=23.9, \ x_0=30, \ y_0=24, and use the given info, we'll

    get: f(30.2,23.9) \approx 50 + (0.2) \times (-0.4) + (-0.1) \times (1.2) = 49.8.
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by Applestar13 View Post
    An Approximation to a partial Derivative

    If a function is known to have
    fx(30,24) = -.4
    fy(30,24) = 1.2
    f(30,24) = 50

    Estimate this value of F.
    f(30.2,23.9)


    Thank you for helping me. I am stuck on the last part
    <br />
  \nabla f(30,24) = \left[ - 0.4,1.2 \right]

    <br />
  f(30.2,23.9) \approx f(30,24) + [0.2, - 0.1].\nabla f(30,24)

    .................. <br />
   = 50 + ( - 0.2 \times 0.4 - 0.1 \times 1.2)  = 49.8<br />

    RonL
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  4. #4
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    Thank you

    Thank you, both of you. That made perfect sense. I didn't know what to do with the difference in the intial value of X and Y.
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