Tangents and area

2010-01-27 4:16 am
The parabola y=-x^2 has two tangents which connect at point P, located on line
y=-x+1. Find the x-coordinate of point P for which the area, S, enclosed by the line connecting the two tangent points and the parabola, is at a minimum.

回答 (2)

2010-01-27 7:31 am
✔ 最佳答案
Please see calculation below:


圖片參考:http://img715.imageshack.us/img715/637/partx1.png

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圖片參考:http://img13.imageshack.us/img13/9909/partx2.png


2010-01-27 00:11:23 補充:
The second part can be done also by considering
(s - t)^2 = (s + t)^2 - 4st
from (3) (s - t)^2 = (s + t)^2 - 2(s + t) + 4
= [(s + t) - 1]^2 + 3
Min (s - t) happens when s + t = 1 so x-ordinate of P = 1/2...
2010-01-27 7:49 am
厲害!


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