# What are the absolute extrema of #f(x)=(2x^3-x)/((x^2-64)# in #[-8,8]# ?

##### 1 Answer

#### Answer:

In

#### Explanation:

The first is an overall graph.

The graph is symmetrical, about O.

The second is for the given limits

graph{((2x^3-x)/(x^2-64)-y)(y-2x)=0 [-160, 160, -80, 80]}

graph{(2x^3-x)/(x^2-64) [-10, 10, -5, 5]}

By actual division,

the slant asymptote y = 2x and

the vertical asymptotes

So, there is no absolute maximum, as

nearly.

x=0. So, origin is the point of inflexion (POI). In

origin, the graph ( in between the asymptotes

in

So, the absolute minimum is 0 at the POI, O.