Find pt of inflexion急thx

Given f(x) = y=(x-2)(x-4) / ((x-3)(x-5)), find the inflection point(s).

Solve

圖片參考：http://i353.photobucket.com/albums/r393/s032015/ScreenHunter_118Oct242223_zps9cf81dd6.jpg


圖片參考：http://i353.photobucket.com/albums/r393/s032015/ScreenHunter_118Oct242224_zps26355953.jpg



Now set the second derivative equal to zero and solve for "x" to find possible inflection points.
4x^3-42x^2+156x-206=0
x=9^(1/3)/2-3/(2*9^(1/3))+7/2

When x < 9^(1/3)/2-3/(2*9^(1/3))+7/2, then f''(x) < 0
When x > 0, then f''(x) > 0

Since f''(x) changes signs at x = 9^(1/3)/2-3/(2*9^(1/3))+7/2, then that is an inflection point.

f(9^(1/3)/2-3/(2*9^(1/3))+7/2) =0.34054143681

圖片參考：http://www4c.wolframalpha.com/Calculate/MSP/MSP11511d3a5g08d9bie55g00003ed0b5b99fa96082?MSPStoreType=image/gif&s=29&w=390.&h=188.&cdf=Coordinates&cdf=Tooltips


2013-10-24 22:38:46 補充：
Image removed so like this:

dy/dx
http://i353.photobucket.com/albums/r393/s032015/ScreenHunter_118Oct242223_zps9cf81dd6.jpg
d^2y/dx^2
http://i353.photobucket.com/albums/r393/s032015/ScreenHunter_118Oct242224_zps26355953.jpg

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