f(x) is increasing where f'(x) > 0.

f(x) is decreasing where f'(x) < 0.

Local maxima and minima occur where f'(x) = 0. If it's a maximum then f''(x) < 0 at that point, and if it's a minimum then f''(x) > 0 at that point.

To sketch the graph, find the critical points, the x and y intercepts and then you have enough info to sketch...