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First we need to choose an interval: Then we can say that a local maximum is the point where: The height of the function at a is greater than (or equal to) the height anywhere else in that interval. Or, more briefly: f(a) â¥ f(x) for all x in the interval. In other words, there is no height greater than f(a).
Actually they are not the same. A peak is a point or an area that is higher than all adjacent areas So it's completely localized, meaning that a mountain can have multiple peaks (In mathematics, it's called local maximum). Summit refers to the highest point in a mountain.he word comes from Latin summus, meaning highest. In the 19th century, summit was also applied to other kinds of highest points, such as the highest point reached when crossing a pass. A peak is a point that's higher than all other adjacent points.