# How would a horizontal line work in the Extreme Value Theorem?

Jun 17, 2015

For a constant function, there is one value of $y$. that value is both the absolute maximum and the absolute minimum.

#### Explanation:

Example:

$f \left(x\right) = 3$ on the interval $\left[2 , 7\right]$ has maximum value 3 and minimum value 3.

All the is required to be the absolute maximum value is that there is no greater value.
All that is requires to be the minimum value is that there is no lesser value.

Also, since, for $f \left(x\right)$ a constant function, we have $f ' \left(x\right) = 0$, every point of the domain is a critical point.

(I am not familiar with the term"turning point", so I don't know whether every point is considered a turning point.)