課程名稱︰微積分甲上
課程性質︰必修
課程教師︰張鎮華老師
開課學院：電資學院等甲一
開課系所︰同上
考試日期（年月日）︰ 101 年 10 月 22 日
考試時限（分鐘）： 30 分鐘
是否需發放獎勵金：是，謝謝您 =)
（如未明確表示，則不予發放）
試題 :
1.(25%) Prove that if f is differentiable on an interval I and f'(x) < a for
all x∈I, then there is at most one point x in I such that f(x)=ax.
2 2
2.(25%) Find a and b such that f(x) = ax/(x +b ) has a local minimum at
x=-3 and f'(0)=4.
3.(25%) Let ABC be a triangle with vertices A = (-4,0), B = (0,8), C = (4,0).
Let P be a point on the line segment that join B to the origin. Find the
position of P that minimizes the sum of distances between P and the three
vertices.
4.(25%) Determine the concavity and the points of inflection (if any) of the
graph of f(x) = 2x + 2x, x∈[0,2π].
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