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Can Cusps Be Maximums?

Elena Rostova • • 6 min read
Can Cusps Be Maximums?

The relative extrema of a function (if any) occur at critical points. But this does not mean that relative extrema occur at every critical point (they could be points of inflection

points of inflection
An inflection point is a point on a curve where the curve changes from being concave (going up, then down) to convex (going down, then up), or the other way around. An undulation point is like an inflection point but the type of curve doesn't change.
, for example). Relative maximums and minimums may occur when the first derivative is not zero (like a cusp).

Can a cusp be an absolute max?

There could possibly be some x = b such that f(b) > f(a) on your interval in which case, your cusp is not a absolute/global maximum.

Can a relative maximum be an absolute maximum?

It is completely possible for a function to not have a relative maximum and/or a relative minimum. ... As this example has shown there can only be a single absolute maximum or absolute minimum value, but they can occur at more than one place in the domain.

Elena Rostova
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Elena Rostova

Elena Rostova holds a Master's degree in Public Health Journalism. She covers groundbreaking medical research, holistic wellness trends, mental health awareness, and nutritional science.