0

From what I have been taught local maxima and minima are calculated for a local interval. From the first derivative test local maxima and minima are calculated for a function, but what is the range(interval) in which these are calculated?

JayMCI
  • 1
  • 1
    Does these help https://www.mathsisfun.com/algebra/functions-maxima-minima.html and https://math.stackexchange.com/questions/1591520/what-is-difference-between-maxima-or-minima-and-global-maxima-or-minima and https://math.stackexchange.com/questions/528624/what-really-are-the-local-maxima-and-local-minima and https://math.stackexchange.com/questions/2134265/can-endpoints-be-local-minimum and https://math.stackexchange.com/questions/1597414/maximum-and-minimum-in-a-range? – Moo Nov 06 '18 at 13:37
  • I'm not sure I understand your question correctly, but $x$ is "local" maximum of $f$ if there is a (often small) positive number $\varepsilon$ such that $f$ is the maximum value over the interval $[x - \varepsilon, x + \varepsilon]$. There's no set minimum value of $\varepsilon$, and it might be extremely tiny, but over a non-trivial interval centred at $x$, the function achieves its maximum at $x$. Does that help? – Theo Bendit Nov 06 '18 at 13:45

0 Answers0