(b) Find f'(x) =_____.

(a) Let u = g(x) = 4 + 3x and y = f(u) = √u. Then = ______.

(b) Let w = ln. Find the differential dw of w.

(a) =__________.

(b) - ... =___________.

(a) Find relative maximum = _____ of f.

(b) Find relative minimum = _____of f.

1. The total weekly revenue (in dollars) of the Country Workshop realized in manufacturing and selling its rolltop desks is given byR(x,y) = -0.2x2 - 0.25y2 - 0.2xy + 200x + 160ywhere xdenotes the number of finished units and y denotes the number of unfinished units manufactured and sold each week. The total weekly cost attributable to the manufacture of these desks is given byC(x,y) = 100x + 70y + 4000dollars. Determine how many finished units and how many unfinished units the company should manufacture each week in order to maximize its profit. What is the maximum profit realizable? (10分)

2. Find the particular solution of differential equationy' = 2 - ythat satisfies the condition y(0) = 3. (10分)

3. Use the second Taylor polynomial of f(x) = ln x at x = 1 to approximate ln 1.1 and find a bound for the error in the approximation. (10分)

4. John Mills - the proprietor of Mills Engine Company, a manufacturer of model air-plane engines - finds that it takes x units of labor and y units of capital to producef(x,y) = 100x3/4y1/4units of the product. If a unit of labor costs $100, a unit of capital costs $200, and $200,000 is budgeted for production. Determine how many units should be expended on labor and how many units should be expended on capital in order to maximize production. (10分)

115年 - 115 中央警察大學_碩士班入學考試試題_海洋科技組：微積分#139855

115年 - 115 中央警察大學_碩士班入學考試試題_消防科學研究所、交通管理研究所：微積分#139760

114年 - 114 臺灣綜合大學系統_學士班轉學生考試試題:微積分A#137897

114年 - 114 臺灣綜合大學系統_學士班轉學生考試試題：微積分B#137819

114年 - 114 台灣聯合大學系統_學士班轉學生考試試題:微積分#137762

114年 - 114 台灣聯合大學系統_學士班轉學生考試試題:微積分#137761

114年 - 114 國立臺灣大學_轉學生招生考試_物理學系/土木工程學系/生物環境系統工程學系/生物機電工程學系:微積分(B)#137745

114年 - 114 國立臺灣大學_轉學生招生考試_數學系:微積分(A)#137744

113年 - 113 國立嘉義大學_轉學生招生考試試題_(全校)：微積分#122986

112年 - 112 國立臺灣大學_碩士班招生考試題：微積分(D)#130254