Determine whether the statement is true or false. If it is true, explain why. If it is

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Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.

There exists a function f with continuous second-order partial derivatives such that f_x(x, y) = x + y² and f_y(x, y) = x − y².

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