(a)

Increasing / decreasing test :

If on the interval, then is increasing on the interval.

If on the interval, then is decreasing on the interval.

Observe the graph.

on the interval and then is increasing on the interval and .

on the interval and , then is decreasing on the interval and .

(b)

First derivative test :

Consider is a critical number of a continuous function .

(i) If changes from positive to negative at , then has a local maximum at .

(ii) If changes from negative to positive at , then has a local minimum at .

(iii) If does not change sign at , then has no local maximum or minimum at .

Observe the graph.

has local maximum at and , because is changing its sign from positive to negative.

has local minimum at , because is changing its sign from negative to positive.

(a)

is increasing on the interval .

is decreasing on the interval and .

(b)

has local maximum at and .

has local minimum at .