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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) =

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) =

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Explain why the function is differentiable at the given point.
f ( x , y ) = 9 + x ln ⁡ ( x y − 5 )
The partial derivatives are f X ( x , y ) = ◻ and f y ( x , y ) = ◻ , so f x ( 2 , 3 ) = ◻ and f y ( 2 , 3 ) = ◻ . Both f x and f y are continuous functions for x y > ◻ 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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