with detailed solution reference : https://drive.google.com/drive/folders/1j4xtb14ojebizLO-owwoJnwTrrDBAvBO

4. The position of a particle moving along a horizontal coordinate line is given by s(t) = t3 - 4t2 - 3t + 6 feet at the end of t seconds, where t 2 0 (3, 1 points) (a) Find the time interval(s) on which the particle is speeding up. (b) How far is the particle from its initial position after 4 seconds? 5. A cylindrical container that is open at the top is to be made from two kinds of material. The material for the side costs 20 pesos per cm? while the material for the base costs 5 pesos per cm2. If the container is to have a volume of 167 cm, what must be its dimensions so that the cost of construction is as small as possible? (5 points) 6. Given F(x) = 4 - t2 dt, evaluate the following. (2, 1 points) (a) F'(-1) (b) F(0), by interpreting F(0) as an area