6. Graph the function according to the given criteria. f (-4) = f(0) =0 f'(x) =0at (-2, 1) f' (x ) > 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) = (x' -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(1) = 0.05t~ +0.2 +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 247 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.Unit 1-2 Assignment Calculus Improvement 2023 Part A: Knowledge 1. Determine the derivative for each of the following. 3 a) y =5x' -4x 2 +6 b ) f (x ) = 19x2 + 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-x 1-x2 4. Determine each limit. a) lim X b) lim x-3 (x - 3)2 194 x-4 Part B: Application 5. The position of a moving particle is given by s(t) = (0.512 -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