Find any relative extrema of the function

This function is defined on and is continuously differentiable on Its derivative is

Let's solve the equation  

both sides are non-negative, hence it may be squared:

which is equivalent to

 or  

This function is defined on and is continuously differentiable on Its derivative is

Let's solve the equation  

both sides are non-negative, hence it may be squared:

which is equivalent to

 or  

This gives us it must be non-negative so only "+" is suitable.

Thus which is and

Now consider the sign of Near it tends to and therefore is positive, at it is negative. Therefore increases from to decreases from to and increases again from to

The answer: is a local one-sided minimum, is a local one-sided maximum, is a local maximum and  is a local minimum.