1. HKCEE 1986
The graph of the function f(x) = x^3 + hx^2 + kx + 2 (h and k are constants) has 2 distinct turning points and intersects the line y = 2 at the point (0,2) only.
(a) Show that 3k < h^2 < 4k
I know h^2 < 4k, but why 3k < h^2 ?
2. HKCEE 1989
http://i233.photobucket.com/albums/ee66/escapefromtheedge/AM_CE19891.gif
I want to ask (a)(iii) "Hence, ... " that part
Answer: (a)(i): T = k√(a^2 + x^2) + (3a - x)
(a)(iii): 1 < k < √10/3 (both)
2 A.Maths Past paper Questions
2007-12-02 9:41 pm
回答 (1)
2007-12-05 10:34 am
✔ 最佳答案
1.2 distinct turning points
=> There are 2 distinct x satisfy f'(x) = 3x^2+2hx+k = 0
=> Discriminant = (2h)^2-4(3)k >0
=> 4h^2>12k
=> h^2>3k
2.
For T= k√(a^2 + x^2) + (3a - x)
now see what x should be chosen.
dT/dx = 0
kx/√(a^2 + x^2) -1 =0
x=a/√(k^2 - 1)
x should be within the range 0 to 3a
so A to B via P is not a choice , i.e. more expensive, if x>3a = b
This yields the same inequality, and the same range of k.
參考: me
收錄日期: 2021-04-23 20:04:59
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20071202000051KK01859