Graph sketching, continuity, differentiation - Is this right?

(I would appreciate either an explanation as to how to solve the problems, or the correct answer so I could figure out what I did wrong.)

1. Let f(x) = 4-x^2 if x __<__ 2

x^2 - 5x + 6 if 2 < x < 3

x if x __>__ 3

a) Sketch the graph of f.

http://img293.imageshack.us/my.php?i...lcgraphgk1.pnghttp://img293.imageshack.us/my.php?image=calcgraphgk1.png

b) At what numbers is f continuous?

- I'm not sure if I did this right, are you supposed to do something with limits to show what numbers are continuous?

(-∞, 2], [2, 3], [3, ∞)

c) At what numbers is f differentiable?

- Again, I've seen in some places where your answer has to include limits. Do you have to use limits in your work or something?

(-∞ ,∞)

d) Give a formula for f'.

f'(x) = 2x if x __<__ 2

2x - 5 if 2 < x < 3

1 if x __>__ 3

2. Let f(x) = x^3 - 9x^2 + 24x + 3

a) For what values of x does the graph of f have a horizontal tangent

- Okay I have no idea what to do for this one. I tried looking through my textbook and couldn't find anything. If someone could show me how to do this, that would be great.

b)

f''(x) = 9