Topics: Derivatives, Differentials and Marginal Analysis. Answer all questions showing steps to justify your answer. You have 90minutes to answer and 15minutes to upload to Moodle as a PDF file Total Points 70 1. Find f '(x) if [15pts.] a) f(x) = 0.2x3 - 3.1x + 13.2 5pts. b) f (x) = (3x - 1)2 5pts. c) f(x) = 10x +20 5pts. X 2. A company manufactures and sells x TVs per month. If the cost and revenue equations are: C(x) = 72000 + 60x R(x) = 200x - 2 Os X S 6000 Then using differentials if production is increase from 4500 to 4510 units per month, find the approximate changes in Profit. [15pts.] 3. A company's total sales (in millions of dollars) t months from now are given by [20pts.] N(t) = 180t t + 4 (a) Use the four-step process or quotient rule to find N'(t) 10pts. (b) Find N(16) and N'(16) Write a brief verbal interpretation of these results. 6pts. (c) Use the results in part (B) to estimate the total sales after 17 months. 4pts. *HINT Four- Step Process: Step 1 Find f(x + h) Step 2 Find f(x + h) - f(x) Step 3 Find f(x + h) - f(x) h Step 4 Find f'(x) = lim f ( x + h ) - f ( x ) h- >0 h Quotient Rule: If f (x) = 1(x) then f'(x) = B(x)T' (x) - T(x) B'(x ) B(x) [B(x) ]