Question

Identify the open intervals on which the function is increasing or decreasing.

Answer 1

Step 1 :

The function is

Domain of the function :

Since there should not be any negative numbers in the square root,

The domain is .

Step 2 :

Let

Apply derivative on each side with respect to x.

Apply the product rule of derivative:

Step 3 :

Determination of critical points:

Since is a root function, it is continuous on its domain .

The critical points exists when .

Equate to zero:

The critical points are .

Consider the test intervals as and .

Thus, The function is increasing on the interval .

And The function is decreasing on the intervals and .

Solution :

The function is increasing on the interval .

The function is decreasing on the intervals and .