Question

g Determine whether the statement is true or false. If fx(a, b) and fy(a, b) both exist, then f is differentiable at (a, b). True False Correct: Your answer is correct.

Answer 1

False

Explanation:

A function is said to be differentiable over a given region if the function is continuous and has only one value for each input.

Therefore in order to conclude that f is differentiable at (a, b), the partial derivatives must be continuous at (a, b).

It is true that the function has to be defined over a given region because without it, you cannot determine if a partial derivative is continuous or otherwise.

But the fact that the partial derivatives exist at a point is not a sufficient condition for continuity.