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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) =

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 ) = x 3 y 2 , ( − 3 , 1 )
The partial derivatives are f x ( x , y ) = ◻ and f y ( x , y ) = ◻ , so f x ( − 3 , 1 ) = ◻ and f y ( − 3 , 1 ) = ◻ . Both f x and f y 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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