Explain why the function is differentiable at the given point. f(x, y)

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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) =

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) = 7 + x \ln (x y - 5), (2, 3)

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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