# Relative Extrema

• Mar 13th 2010, 08:33 AM
yomath
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
• Mar 13th 2010, 09:36 AM
CaptainBlack
Quote:

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:

\$\displaystyle G'(x)=0\$

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

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

CB