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Math Help - estimates based on partial derivatives

  1. #1
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    estimates based on partial derivatives

    hello
    ive got a quiz tomorrow, and this is one of the example questions
    i have looked through my text and my notes, and havent found anything that could help me.

    Suppose that is a smooth function and that its partial derivatives have the values, and . Given that , use this information to estimate the following values:

    Estimate of (integer value)
    Estimate of (integer value)
    Estimate of (integer value)

    at first I was trying to come up with a function that would satisfy that derivatives and the function, but it turned out to be harder than i thought. what do i need to do?
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  2. #2
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    Use linear approximation: f(0,-7) = f(0,-8+1) \approx f(0,-8) + 1\cdot f_y(0,-8)
    Now substitute the numerical values.
    Do the same thing with other ones.
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  3. #3
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    ah thank you!
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