se the function to show that fx(0, 0) and fy(0, 0) both exist, but that f is not differentiable at (0, 0). f(x, y) = 9x2y x4 + y
2 , (x, y) ≠ (0, 0) 0, (x, y) = (0, 0)
1 answer:
Answer:
It is proved that exixts at (0,0) but not differentiable there.
Step-by-step explanation:
Given function is,
- To show exixtance of we take,
exists.
And,
exists.
- To show f(x,y) is not differentiable at the origin cheaking continuity at origin be such that,
where m is a variable.
which depends on various values of m, therefore limit does not exists. So f(x,y) is not continuous at (0,0). Hence it is not differentiable at (0,0).
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