Disentangling local maxima, local minima, global maxima and global minima.
In the graph above the point represents an (x,y) such that the y-coordinate is the lowest it can be within the small neighborhood shown around the point. So it’s a local minimum of y=1 at x=6.
In the picture right above the
In this image we see that the point (6,1) is such that on the left side there are many points with lower y coordinates. Specifically, we can slide down the left side of the graph forever, meaning there is no lowest y coordinate. In other words, there is no global minimum. In the graph above we see on the right there are points whose y-coordinate is more than 7. We can just slide up the graph forever, meaning there is no highest y-coordinate. In other words, there is no global maximum. We have to imagine the graph goes up towards positive infinity in terms of y forever. It doesn’t end, but we can’t show this in a picture.
