OK, its been a while, but I'll take a crack at it.
Going from f'(x) to f(x).
- Any point f'(x) = 0, f(x) has a turning point.
- Where f'(x) > 0 (above the x-axis), the slope on f(x) graph will be "going up", left to right. Conversely, when f'(x) < 0, the slope on f(x) graph will be "going down", as the gradient (f'(x) is the gradient) is negative.
This should get you started, I think. Use the same principles to go from f''(x) to f'(x) (and then f(x), if neccessary).
Also, when f'(x) = 0, and is a turning point; ie- f'(a) = 0 and f''(a) = 0, then f(a) is a point of inflexion.
Lastly, I don't think your y-intercept will matter in some occassions. They may give you more information, in that regard.
Like I said, it has been a while. So, maybe someone will correct me if I have made a mistake.