# : Use the function to show that f,(0, 0) and fy(0, 0) both exist, but that f is not differentiable at (0, 0). 7x3y x4

: Use the function to show that f,(0, 0) and fy(0, 0) both exist, but that f is not differentiable at (0, 0).
7x3y
x4 + y2
0,
f(x, y) =
(x, y) # (0, 0)
(х, у) %3D (0, 0)
=
fx(0, 0) =
fy(0, 0) =
Along the line
lim
(x, y) → (0, 0)
y = x
Along the curve
y = x2
lim
(x, y) → (0, 0)
O f is continuous at (0, 0)
O f is not continuous at (0, 0)

(550 words)

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