# derivative result constant function: maximum or minimum?

i need some help.

I got $y=2x+5$

Derivative $y'= 2$

So far so good.

My question:

There is a maximum or minimum ?

• $y'=2$ says (or, rather, confirms) that it's a linear function. $y' \gt 0$ says it's a strictly increasing function. Do either of those two types of functions have a maximum or minimum on $\mathbb{R}$?
– dxiv
Nov 23 '16 at 5:18
• This depends. On a closed interval, $[a,b]$, for example, there is a maximum, namely $2b + 5$. On open intervals (or the entire set of real numbers) however there is no maximum. Nov 23 '16 at 5:44

As $y( x)$ is continous and increasing ($y'> 0$ for all $x \in Dom (f)$) then if $y (x)$ is definite on a compact this is maximum in the right extreme. In other hand, if $Dom (f)=\mathbb{R}$ it's false.
No, there is are no extrema. Think conceptually about what a derivative means. $y' = 2$ says that the the function y(x) is increasing twice as fast as the variable x for every value of x. This is cemented by the fact that $y'' = 0$, so that the relation is permanent. I.e. the slope does not change. Indeed, this describes a straight line, which of course has no maximum nor minimum.