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Yahoo!奇摩知識+ - 分類問答 - 科學常識 - 已解決
Yahoo!奇摩知識+ - 分類問答 - 科學常識 - 已解決 
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高一數學函數
Oct 1st 2013, 13:59

f(x)=(x²+3x+1)(x²+3x+2)+3x²+9x+8
另A=x²+3x 代入f(x)
⇒f(x)=(A+1)(A+2)+3A+8
展開化簡
⇒f(x)=A²+6A+10
⇒f(x)=(A+3)²+1
當(A+3)²越小f(x)的值越小
A=x²+3x代入(A+3)²
⇒(x²+3x+3)²⇒當x²+3x+3的值越接近0則(x²+3x+3)²的值越小
故只討論x²+3x+3⇒化簡
⇒(x+1.5)²+0.75⇒當x=(-1.5)時有最接近0的數0.75
x=(-1.5)代入f(x)=(x²+3x+2)²+1得到最小值1
故f(x)=(x²+3x+1)(x²+3x+2)+3x²+9x+8之最小值=1

這我自己解的因為我也是高一
所以如果有誤請告知我一下

參考資料： 自己

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