1. The function f(x) is defined for all x and its derivative f (x) has the following properties:

1. f (x) is differentiable for all x,

2. f (1) = f (3) = 0,

3. f (x) has an absolute maximum at x = 2,

4. f (x) decreases on the interval (, 2) and increases on the interval (2, ).

Find the following (make sure to justify your answers):

(a) the interval(s) where f(x) increases.

(b) the interval(s) where f(x) decreases.

(c) the local maxima and minima of f(x).

(d) the interval(s) where f(x) is concave up.

(e) the interval(s) where f(x) is concave down.

(f) the points of inflection of f(x).

2.