# exercise with arctg and (probably) differntial

#### Kangurur

##### New member
$$\displaystyle xarctgx>(1/2) (pi)-1$$

$$\displaystyle x>=0$$
I have no idea how to solve this. Help me please

#### HallsofIvy

##### Elite Member
This does NOT involve a differential and certainly is NOT a differential equation! There is no "formula" or "trick" to this, just look for values of x so that $$\displaystyle x arctan(x)= 0$$. It is simply algebra- solve this equation.

I would start by using "Desmos", https://www.desmos.com/calculator, to graph $$\displaystyle y= x arctan(x)$$ and $$\displaystyle y= \frac{\pi}{2}- 1$$. It appears that $$\displaystyle x arctan(x)>\frac{\pi}{2}$$ for x< -0.826 and x> 0.826, approximately.