Calculus section derivatives

10. The motion of a particle is described by the position function 3(t) = 2153 15$2 + 33t + 17, t > 0 where t is measured in days and 3(t) in millimetres. a. When is the particle at rest? [4 marks] b. When is the velocity positive? [4 marks] c. Draw a diagram, or describe a diagram in words, to illustrate the motion of the particle in the rst 5 days. [3 marks] d. Find the total distance travelled in the rst 5 days. [3 marks] 11. Asnowball melts so that its radius decreases by 0.2 cmfmin. Find the rate at which the surface area decreases when the radius is 4 cm. (SA = 4111"?!) [6 marks] 12. For the function rs) = (13:3 + bx2 53: + 9. determine the values ofa and b so that f(l) = 12 and f'(].) = 3. [5 marks]