# How do you sketch the graph by determining all relative max and min, inflection points, finding intervals of increasing, decreasing and any asymptotes given #f(x)=(x-4)^2/(x^2-4)#?

##### 1 Answer

Relative maximum

#### Explanation:

I took 30' for this answer. I should have a break. Please make another answer, without attempting to edit my answer. After some time, I would edit my answer, myself.. I have to repeat this because some rush to supply typo omissions of characters like #. I would do it myself. Logical and computational errors can be pointed out in the comment column and not by editing my answer. .

graph{(x-4)^2/(x^2-4) [-30, 30, -15, 15]}

x-intercept ( y = 0) : 4

y-intercept ( x = 0 ) :

By actual division and resolving into partial fractions,

As

#=0, when x = 1 and 4,

Local minimum

Local maximum :

nearly

So, the POI is at x = 5.034, nearly