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)