Question

#49 graph in desmos and label points of inflection, critical points, local extremes, absolute extremes, asymptotes, etc

Answer 1

Kindly check below.

1) Let's plot that polynomial and identify the inflection, critical points, extreme points, and further information as requested.

2) We can plot that and label these points below.

Note on the graph, that the inflection point defines the point where the graph starts to change its concavity. We can see the Maximum and the minimum point between them.

In addition to this, there are no asymptotes for functions like these.

`\begin{gathered} Inflection\:point\:at:(2,-(40)/(3)) \\ \\ Maximum\:at:\:(-1,\:(14)/(3)) \\ \\ Minimum\:at:\:(5,-(94)/(3)) \\ \\ x=-1,x=5\:Critical\:Points \end{gathered}`

3) Thus, this is the answer.