I once read a suggestion to explain the difference between local and global maxima by using the example of Mount Everest (global maximum of the height function) and K2 (local maximum). I consider this a bad example because it gives two erroneous impressions: (1) local maxima almost achieve the global maximum value (because K2 is almost as high as Everest) and (2) local maxima occur at locations very near the global maximum (because K2 is essentially right next to Everest). A much better example of a local maximum of height would be Mount Brighton (a ski hill about 50 miles from Ann Arbor --- built on a lanfill, if I remember correctly). Students need to learn that, if you want a global maximum and you find a local maximum instead, you can be wildly wrong.

I once read a suggestion to explain the difference between local and global maxima by using the example of Mount Everest (global maximum of the height function) and K2 (local maximum). I consider this a bad example because it gives two erroneous impressions: (1) local maxima almost achieve the global maximum value (because K2 is almost as high as Everest) and (2) local maxima occur at locations very near the global maximum (because K2 is essentially right next to Everest). A much better example of a local maximum of height would be Mount Brighton (a ski hill about 50 miles from Ann Arbor --- built on a landfill, if I remember correctly). Students need to learn that, if you want a global maximum and you find a local maximum instead, you can be wildly wrong.