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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) =

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 ) = x 6 e y , ( 1 , 0 )
The partial derivatives are f x ( x , y ) = ◻ and f y ( x , y ) = ◻ , so f x ( 1 , 0 ) = ◻ and f y ( 1 , 0 ) = ◻ . Both f x and f y 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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