Please answer the questions below fully and completely. Be sure to show your steps, use correct notation, and make your work clear. It is expected that you attempt each problem and if you get stuck, explain your uncertainty. Remember that fixes cannot be made on problems that have no attempt and/or explanation of the sticking point for you. 1. Please take the derivatives of the functions in a-c. Work must be shown. Meaning a derivative listed with no work, or incorrect work leading up to a correct derivative, would not earn full credit. You may use shortcut derivative methods. a. f(x) = x tan (3x + 1) b. w(t) = 21n (cos (4t)\f3. The cost, in dollars, of producing yards of a certain fabric is modeled by C(x) = 1200 + 12x - 0.1x2 (a) Find the marginal cost function. You have permission to look up what marginal cost is (in general), if you are unsure. (b) Find C'(200) and explain its meaning. What does it predict