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An "extreme value" is either a local maximum, or a local minimum - i.e., a point which is greater than all the points in a certain neighborhood, or less than all points in a certain neighborhood.
There are infinitely many points in a plane.
I believe the correct term is "extrema" not "extreme." But anyway, extrema are the lowest or highest points on a graph. All other points are higher than the minima, and all other points are lower than the maxima. In the graph y=x2, (0, 0) is the minima because that is the lowest extent of the range of that graph. There is no maxima because the y value will increase to infinity.
243 points.