Step 1 :

Concavity test:

(a) If for all x in I, then the graph of f is concave upward on I.

(b) If for all x in I, then the graph of f is concave downward on I.

Step 2 :

The function is .

Differentiate  with respect to x.

Step 2 :

Differentiate  with respect to x.

Step 3 :

Determination of inflection points : 

Equate to zero.

Thus, the inflection points are .

Consider the test intervals as and .

\ Interval \	Test Value	Sign of	Concavity
		\ \	Up
		\ \	Down
		\ \	\ Up \

Thus, the graph is concave up in the interval and .

The graph is concave down in the interval .

Solution :

The function is concave up in the interval and .

The function is concave down in the interval .