Question

Anybody know how to find point with zero gradient in contour plot?

Answer 1

Maxima: nearby gradient vectors all point toward the critical point (function increasing)

Minima: nearby gradient vectors all point away from critical point (function decreasing)

Saddles: some nearby gradients point toward, others away.

Answer 2

The gradient is the 3d equivalent of slope from 2d calculus. The gradient is zero at a minima or maxima. (because at that point the slope is neither increasing (+) nor decreasing (-)) So looking at your contour plot... where is the minima (or maxima)? That's where the gradient is zero.

Answer 3

@mathteacher1729 shouldn't that be around [0.3,0.3] in above contour plot?

Answer 4

@SUROJ Yes, that sounds about right. You'd need more contour lines to be sure,though.