What are local extrema?

1 Answer
Alan N.
Dec 13, 2016

Points on some function where a local maximum or minimum value occurs. For a continuous function over its entire domain, these points exist where the slope of the function #=0# (i.e it's first derivative is equal to 0).

Explanation:

Consider some continuous function #f(x)#

The slope of #f(x)# is equal to zero where #f'(x)=0# at some point #(a, f(a))#. Then #f(a)# will be a local extreme value (maximim or minimum) of #f(x)#

N.B. Absolute extrema are a subset of local extrema. These are the points where #f(a)# is the extreme value of #f(x)# over its entire domain.

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