# Thread: Relative Extrema

1. ## Relative Extrema

The class I am taking is called Brief Calculus - I am uncertain if this is the correct forum to post this question. I am certain someone will tell me if I'm in the wrong location. It is an online class and I cannot locate any help in either the textbook or none of the on-line examples are in this format. The first step in the problem is really where I am struggling. Any help would be appreciated

Find the x-value of all points wher the function below has any relative extrema Find the value(s) of any relative extrema.

G(x) = 6x + 7x^ 6/7

2. Originally Posted by yomath
The class I am taking is called Brief Calculus - I am uncertain if this is the correct forum to post this question. I am certain someone will tell me if I'm in the wrong location. It is an online class and I cannot locate any help in either the textbook or none of the on-line examples are in this format. The first step in the problem is really where I am struggling. Any help would be appreciated

Find the x-value of all points wher the function below has any relative extrema Find the value(s) of any relative extrema.

G(x) = 6x + 7x^ 6/7
Relative extrema are also know as local extrema, and are roots of:

$G'(x)=0$

Not all of the roots of this are extrema, they may be points of inflection, if $G''(x)>0$ then you have a local/relative minimum and if $G''(x)<0$ you have a local/relative maximum, where $x$ is a root of $G(x)$. This is known as the second derivative test.

All of this will be in your notes, text or online help somewhere.

CB