So you know that points A, B and C are on the x-axis. This means that at these points, y=0. So make the equation:
0=x^3-4x^2+3x.
Then you can factor this by removing an x from the equation to get:
0= x(x^-4x+3) which is equal to 0=x(x-3)(x-1)
from this, you know that x=0, x=3, x=1. This is the answer to (a).
For (b), you have to differentiate. So,
dy/dx = 3x^2-8x+3
then substitute x=0 and you get an answer of 3 for the gradient, substitute x=3 and you get 6 and substitute x=1 and you get -2.
Hope that made sense!