Suppose a function z (x, y) satisfies the criteria for the test for relative extrema at a point (a, b), and xx (a, b) 0, while yy (a, b) 0 What does this tell you about (a, b) Based on the sign of xx (a, b) and yy (a, b), why does this seem intuitively plausible ...

This tells us that a b is a saddle point The sign ...

Suppose a function z = (x, y) satisfies the criteria for the test for relative extrema at

Question:

Suppose a function z = ƒ(x, y) satisfies the criteria for the test for relative extrema at a point (a, b), and ƒ_xx(a, b) > 0, while ƒ_yy(a, b) < 0. What does this tell you about ƒ(a, b)? Based on the sign of ƒ_xx(a, b) and ƒ_yy(a, b), why does this seem intuitively plausible?

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