Sign of a second partial derivative

LCSphysicist · Jul 29, 2020

3D surface plot of z = f(x, y) with axes x, y and z, showing a saddle-shaped surface; two marked points at (1, 2) and (-1, 2) are labelled, with parts (a) f_xy(1, 2) and (b) f_xy(-1, 2) below.

I am not sure how to determine the sign of this derivatives.
(a) first we can pass a plane by (1,2) parallel to XZ (y fixed) and see how the curve belongs to the plane will vary with x, but what about the next partial derivative, with respect to y?

FactChecker · Jul 30, 2020

At the point, look at the slope with respect to x. When the point moves slightly in the positive y direction, does the slope with respect to x increase or decrease?

Sign of a second partial derivative

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