21, 22, & 23

21. [-/3 Points] DETAILS SCALC8 2.7.508.XP. The cost function for production of a commodity is C(x) = 301 + 23x - 0.05x2 + 0.0001x3. (a) Find C'(100). Interpret C'(100). This is the number of items that must be produced before the costs reach 100. This is the cost of making 100 items. O This is the amount of time, in minutes, it takes to produce 100 items. O This is the rate at which the production level is decreasing with respect to the cost when x = 100. O This is the rate at which costs are increasing with respect to the production level when x = 100. (b) Find the actual cost of producing the 101st item. (Round your answer to the nearest cent.) $ 22. [-/1 Points] DETAILS SCALC8 2.8.501.XP. If y = 4x3 + 2x and OX = 2, find dy when x = 3. dy =[ dt 23. [-/1 Points] DETAILS SCALC8 2.8.504.XP. A particle is moving along the curve below. y = Vx cm/s As the particle passes through the point (4, 2), its x-coordinate increases at a rate of 5 cm/s. How fast is the distance from the particle to the origin changing at this instant? (Roun 24. [1/2 Points]