Goddyx Inc. manufactures bicycle toothbrushes. The cost of manufacturing a toothbrushes in one day is C(x) dollars, where C(x) = 10.0002x3 + 1000Vr + 2344. In On October 2021, Goddyx Inc. made 100 toothbrushes. Answer each of the following parts with a complete English sentence. (a) [1pt] How much did it cost Goddyx Inc. (in dollars) to manufacture 100 toothbrushes on October 9, 2021? (b) [3pt] What was the marginal cost C"(100) (in dollars per toothbrush) in on October 9, 2021? (c) [1pt] What was the average cost, C(100), (in dollars per toothbrush) of manufacturing each toothbrush On October 9, 2021? (Hint: Use part (a).){d} [3pt] The marginal average cost C"{x} is the rate of change of 0(a) = gig; with respect to .12. Use your above answers to compute the marginal average cost (in dollars per toothbrush per toothbrush) for God- dyx Inc. on October 9, 2021. (Hint: You should not have to evaluate another square root to answer this!) (e) [21M Goddyx Inc. is considering increasing the number of toothbrushes manufactured each day from 100 to 100 + Act. In part ((1), you should have found that the marginal average cost @1100} is a negative num- ber, so the average cost of manufacturing each toothbrush should decrease when Am is a small positive number. More precisely, since _ _ (31100): 11111 C(100+ Ax) CHOU) AzNZJ' Ax we expect that, for small values of Am, the change in the average cost can be approximated as follows. C(IUO + As) (31100) a @000) - As: (dollars per toothbrush). i. Use this fact and part (d) to approximate how much the average cost of manufacturing each tooth- brush will decrease if Goddyx Inc. increases its production from 100 to 103 toothbrushes per day. ii. Find the exact decrease in average cost, C(IUO) (31103}, (to the nearest hundredth of a cent) by using part (c) and a calculator