作者jane050177 (半分の月が辉いていた)
看板NTUBIME100HW
标题[转录][试题] 95上 黄汉水 微积分甲上 第二次小考
时间Sun Nov 11 12:26:22 2007
※ [本文转录自 NTU-Exam 看板]
作者: ptt789789 (好烦喔~~~) 看板: NTU-Exam
标题: [试题] 95上 黄汉水 微积分甲上 第二次小考
时间: Sat Nov 10 12:19:41 2007
课程名称︰微积分甲(上)
课程性质︰系定必修
课程教师︰黄汉水
开课学院：生机、生工、地质、公管
开课系所︰数学系
考试日期（年月日）︰2006/11/17
考试时限（分钟）：70分钟
是否需发放奖励金：是
（如未明确表示，则不予发放）
试题 :
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％)
_______
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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