[Math] Finding extrema, non-critical points, and saddle points given a contour plot

graphing-functionsmultivariable-calculus

I'm trying to interpret the contour plot as like a mountain, where all the segregated areas are plains that are higher when it proceeds inwards. What is the significance of the numbers on x-axis and y-axis, and wouldn't the points that are most centered be maximums?

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Best Answer

The general idea is:

  1. When a point is surrounded by concentric closed contour lines, it have to be a extrema, because as you cross the contour lines, the height is continuously changing, and at the center you will get the zero change.

  2. When two contour lines cross their is a saddle point.

  3. Neither of two stated happens, then it is non-critical point.

So here, points B, D are extrema, A is saddle point, and C is non-critical point.

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