Problem 51

Step 1.

The given function is

 

We need to find on what interval is this function increasing.

To do this, we need to find the first derivative of this function,  , and to find the values of   for which .

Applying The Product Rule

 

and The Power Rule

 

knowing that , we obtain

$  

Notice that the function sign depends only on the member  

So, we can conclude that   for  .

Therefore, we can conclude that   is increasing on the interval  , which we see from the graph below.