Unit 2 Assignment: Derivatives I19 I. [4 points) Determine the equation of the tangent line to the polynomial f{x) = 3x3 + 2):2 x + 5 at the point [3. 55]. 2. One of Ramsay Bolton's archers res an arrow into the air towards Ion Snow. 11's height in metres. after t seconds is given by h[t] = 4.9t2 + 27.5t + 1.25 [a] {2 po inrs] Determine the speed of the arrow after 2 seconds. (in) [2 points] How long is the arrow in the air when it hits the ground? [c] [2 points] How fast was the arrow moving when it hit the ground? 3. [4 points) Determine the equation of the tangent at x = 3 for fixl : m- 4. Cersei drains Wildre {a a mmable liquid] out from under the Red Keep fora nefarious deed. The volume of the holding tank can be modelled by the in nctio n: I 2 we) 3ouo (1 E) [a] {2 points] How mam.r litres are in the tank aer 2 hours? (b) [3 points] How fast is the Wildre draining from the tank after 5 hours