課程名稱︰微積分甲(上)
課程性質︰系定必修
課程教師︰黃漢水
開課學院：生機、生工、地質、公管
開課系所︰數學系
考試日期（年月日）︰2006/11/17
考試時限（分鐘）：70分鐘
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
一 Let f(x)=x^5-10x^3+25x-16
(1)Sketch the graph of the function y=f(x) (20％)
(2)Find the absolutely maximum value and the absolutely minimum value
of the function f(x) on the closed interval [-2,3] (10％)
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二 Let f(x)=√(x^2-4)
(1)Find equation of the tangent line L of the graph of y=f(x) at
(a,f(a)) where a>2 (15％)
(2)Find the area of the triangular region bounded by the tangent line L
y=x and y=-x (15％)
三 The curve y=ax^2+bx+c passes through (4,31)
Suppose that y=6x-5 is the tangent line of the curve at (2,7)
Find a,b and c (20％)
四 Let f(x)=x^3-3bx+c (20％)
Find necessary and sufficient conditions on b and c such that
the equation f(x)=0 has three distinct real roots
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