Question: A friend taking calculus is puzzled. She remembers that for a function of one variable, if the first derivative is zero at a point and

A friend taking calculus is puzzled. She remembers that for a function of one variable, if the first derivative is zero at a point and the second derivative is positive, then there must be a relative minimum at the point. She doesn’t understand why that isn’t true for a function of two variables—that is, why ƒ_x(x, y2) = 0 and ƒ_xx(x, y2) > 0 doesn’t guarantee a relative minimum. Provide an explanation.

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