2:39 all 4G AA A smileldcsbon-my.sharepoint.com C . . . 0 , x -2 f " (4) = f"(2) = f" (-1)=0 f"(x)0, -1 4 7. Determine the critical points and inflection points for the following function. f (x) = (x3-1)3 8. An environmental study of a suburban community suggests that t years from now, the average level of carbon monoxide in the air will be q(t) =0.05t +0.2t +3.1 parts per million. When will the rate of carbon monoxide level be changing at 0.775 parts per million/year? (Decimals permitted) Part C: Thinking 9. The chipmunk population in a wooded area can be modeled by the function p(t) = v350t + 50t2 , where p is the number of chipmunks and t is the time in years. Determine the rate of change when the population is 145 chipmunks. Decimal work is permitted. 10. Let f(x) = ax +bx +cx+d. Determine the values of a, b, c and d if f(x) has critical points at x = -1 and x = 2, f(0) = 1 and f '(0) = 6. 11. A cylindrical container is open on the top and has a capacity of 2417 cm . If the cost of the material used for the bottom of the container is $3/cm and the material for the curved part is $1/cm, determine the dimensions of the container that will minimize the cost. m2:41 C all 4G AA A smileldcsbon-my.sharepoint.com C . . . GD Info 1 DI X Unit 1-2 Assignment Calculus Improvement 2023 Part A: Knowledge 1. Determine the derivative for each of the following. a) y =5x' -4x 2 +6 b) f (x ) = 3 (9x2 + 4 c ) f ( x ) = 1+ x2 Show the first line only! No need to simplify. 2. Find the equation of a line (in standard form) that is perpendicular to the tangent line to y = x3 - 5x + 2 at the point (2, 0). 3. Determine any holes or asymptotes for the following function, if they exist. f ( x ) = 1-x3 1 - x 2 4. Determine each limit. a) lim - X b) lim x - 6 x-3 (x - 3)2 x-4* x - 4 Part B: Application 5. The position of a moving particle is given by s(t) = (0.5t -2t) where s is measured in metres and t is in seconds. a) Find the velocity of the particle at 3 seconds? b) When is the particle at rest? 6. Gr 1 12 Q f ( 4 ) . .. f'(x) =0at (-2. 1) m