A point, or value, which is a maximum or a minimum(noun)
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Use "extremum" in a sentence
"And the value of E at the extremum is the entropy itself!"
"To see where this will lead, one can take the derivative of D with respect to y, and set it to zero to find the extremum which is indeed a minimum, but I’ll leave that detail to the reader:"
"Options markets have a volatility 'smile': the implied volatilities of the extremum strike prices are much higher than implied by gaussian distributions."