##### 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.**

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