f(x, y) = x³ex, (1, 0) The partial derivatives are f(x, y) = Find the linearization L(x, y) of the function at (1, 0). L(x, y) = and fy(x, y) = , so fx(1, 0) = and f,(1, 0) = [ . Both fx and fy are continuous functions, so f is differentiable at (1, 0).

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Explain why the function is differentiable at the given point.
f(x, y) = x³ey, (1, 0)
The partial derivatives are f(x, y) =
Find the linearization L(x, y) of the function at (1, 0).
L(x, y) =
and f(x, y) =
, so fx(1, 0) =
and f(1, 0) = [
Both fx and fy are continuous functions, so f is differentiable at (1, 0).
Transcribed Image Text:Explain why the function is differentiable at the given point. f(x, y) = x³ey, (1, 0) The partial derivatives are f(x, y) = Find the linearization L(x, y) of the function at (1, 0). L(x, y) = and f(x, y) = , so fx(1, 0) = and f(1, 0) = [ Both fx and fy are continuous functions, so f is differentiable at (1, 0).
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