Asked by: Nestor Espriu
asked in category: General Last Updated: 2nd April, 2020

What are extreme values of a function?

Extreme Value Theorem. The Extreme Value Theorem guarantees both a maximum and minimum value for a function under certain conditions. It states the following: If a function f(x) is continuous on a closed interval [ a, b], then f(x) has both a maximum and minimum value on [ a, b].

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In respect to this, how do you find the extreme value of a function?

To find extreme values of a function f , set f'(x)=0 and solve. This gives you the x-coordinates of the extreme values/ local maxs and mins. For example. consider f(x)=x2−6x+5 .

Also Know, what are extreme points of a function? The maximum value of the function f (x) = cos x is y = 1: Extreme points, also called extrema, are places where a function takes on an extreme value—that is, a value that is especially small or especially large in comparison to other nearby values of the function.

Keeping this in view, what are the extreme values?

An extreme value, or extremum (plural extrema), is the smallest (minimum) or largest (maximum) value of a function, either in an arbitrarily small neighborhood of a point in the function's domain — in which case it is called a relative or local extremum — or on a given set contained in the domain (perhaps all of it) —

How do you prove a function is continuous?

If a function f is continuous at x = a then we must have the following three conditions.

  1. f(a) is defined; in other words, a is in the domain of f.
  2. The limit. must exist.
  3. The two numbers in 1. and 2., f(a) and L, must be equal.

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