Higher Order Derivatives problem involving the position of a particle

Question

Given the position of a particle is $$s(t)=t^3-12t^2+36t-20$$

a. Find the velocity and acceleration functions

b. When is the particle moving to the right?

c. When is the particle speeding up?

Here is my work. I am particularly concerned with parts b and c of this question. Have I solved this correctly?

Note that my answer for part c. should read 'when $t>4$'

Answer 1

Part $a$ looks good!
For part $b$ you must get two intervals. See if you can use below hint $$ab \gt 0 \implies (a\gt 0 \text{ and } b\gt 0) \text{ or } (\color{blue}{a\lt 0 \text{ and } b\lt 0})$$