• Math Archive: Questions from 2024-10-22

    Explain why the function is differentiable at the given point. f(x, y) = 7 + xln⁡(xy−5), (2, 3) The partial derivatives are fx(x, y) = and fy(x, y) = , so fx(2, 3) = and fy(2, 3) = . Both fx and fy are continuous functions for xy > and f is differentiable at (2, 3). Find the linearization L(x, y) of f(x, y) at (2, 3). L(x, y) =
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    Explain why the function is differentiable at the given point. f(x, y) = x6ey, (1, 0) The partial derivatives are fx(x, y) = and fy(x, y) = , so fx(1, 0) = and fy(1, 0) = . Both fx and fy are continuous functions, so f is differentiable at (1, 0). Find the linearization L(x, y) of the function at (1, 0). L(x, y) =
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    Explain why the function is differentiable at the given point. f(x, y) = x3y2, (−3, 1) The partial derivatives are fx(x, y) = and fy(x, y) = , so fx(−3, 1) = and fy(−3, 1) = . Both fx and fy are continuous functions, so f is differentiable at (−3, 1). Find the linearization L(x, y) of the function at (−3, 1). L(x, y) =
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    Explain why the function is differentiable at the given point. f(x, y) = 9 + xln⁡(xy − 5) The partial derivatives are fx(x, y) = and fy(x, y) = , so fx(2, 3) = and fy(2, 3) = . Both fx and fy are continuous functions for xy > and f is differentiable at (2, 3). Find the linearization L(x, y) of f(x, y) at (2, 3). L(x, y) =
    0 answer