# How do you graph #f(x) = 2x arctan(x-1)#?

##### 2 Answers

By viewing my lengthy answer , the reader can understand why this question remained unanswered, for years.

#### Explanation:

Conventional range for

Correspondingly,

The graph has terminals, at

for transcendental x = 0.5327.

See graph, revealing this approximation.

Graph for y':

graph{y-arctan(x-1)-x/((x-1)^2+1)=0 [.532 0.533 -.01 0.01]}

The turning point is near ( 0.5327, -0.4186 )#

See graph of the given equation that reveals this,

but not the terminals.

graph{(y-2x arctan(x-1))((x-0.53)^2+(y+0.418)^2-0.01)=0}

Now see graph for

graph{y-2x arctan(x-1)=0 [-1 3 0 6]}

Now, see graph for

graph{y-2x arctan(x-1)=0 [0 1 -0.6 0]}

Sliding these graphs,

you could see graph extending.

terminals that are created by limits imposed on

values.

Continued in the 2nd answer, .

.

Continuation, for the 2nd part. I would review my answer and improve/correct, if necessary. Please avoid editing my answer.

#### Explanation:

My calculator displays

In this 21st century, it is not impossible to return

I expect this happen soon.

Here, I define

for

Here, the inverse

Graph of

using the wholesome inverse

This includes the 1st part graph, for the conventional

graph{x - 1 - tan( y / (2 x ))=0}.

Is the graph cumbersone? I do not think so.

Slide the graph

me.

Interestingly, x = 1, for y = even

Respectively,

graph{(x - 1 - tan( y / (2 x )))(x-1 +0y)=0}.