help?derivatives? shape of? concave up-concave down?

Question

Answer 1

(8)

Step 1:

Concavity test :

If for all x in the interval, then the graph of f  is concave upward on the interval.

If for all x in the interval, then the graph of f  is concave downward on the interval.

Observe the graph .

over the intervals   and , therefore the function is concave upward on the intervals and .

over the intervals   and , therefore the function is concave downward on the intervals and .

Solution :

The function is concave upward over the intervals and .

The function is concave downward over the intervals and .

Answer 2

(9)

Step 1:

Concavity test :

If for all x in the interval, then the graph of f  is concave upward on the interval.

If for all x in the interval, then the graph of f  is concave downward on the interval.

Observe the graph .

over the intervals   and , therefore the function is concave upward on the intervals and .

over the interval , therefore the function is concave downward on the interval .

Solution :

The function is concave upward over the intervals and .

The function is concave downward over the interval .