作者  ajenny13 (~~~)                                          看板  NTU-Exam 
 標題  [試題] 103-1 周青松 微積分甲上 期中考                                  
 時間  Wed Dec 10 09:44:55 2014                                               
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課程名稱︰微積分甲上
課程性質︰必修
課程教師︰周青松
開課學院：理學院
開課系所︰數學系
考試日期（年月日）︰103年11月10日
考試時限（分鐘）：110分鐘

試題 :
(1)Determine the discontinuities of the following function and sketch the graph
      {2x+1,   x≦0
f(x)= {1,      0<x≦1
      {x^2+1,  x>1

(2)Find the second derivative of y=x^1/2 tan(x^1/2)

(3)Find the local minimum of f(x)=x^4-2x^3 and sketch the graph

(4)Find the critical points of the function and classify all the extreme
values also sketch the graph

f(x)={x^2+2x=2,  -1/2≦x<0
     {x^2-2x+2,  0≦x≦2

(5)Find the points of inflection of f(x)=x^3-6x^2+9x+1 and sketch the graph

(6)Find f'(-3) and f'(1) given that

f(x)={x^2,   x≦1
     {2x-1,  x>1


(7)Determine the region of the function where g increase, and sketch the
graph
g(x)={x/2+2,  x<1
     {x^3,    x≧1

(8)Suppose that f(x)=Ax^2+Bx+C has a local minimum at x=2 and the graph
passes through the points (-1,3) and (3,-1). Find A, B, C.

(9)Find the critical points of the function and classify all the extreme
values
     {2-2x-x^2,    -2≦x≦0
f(x)={｜x-2｜,       0<x<3
     {1/3(x-2)^3,  -3≦x<4

(10)Determine A and B so that the curve y=Acos2x+Bsin3x has a point of
inflection at (π/6, 5)

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