[解題] 三角函數求極值
1.年級：高一
2.科目：數學
3.章節：高一下第三章三角函數
4.題目：
f(x)=(sinx*cosx)/(1+sinx+cosx)
前面小括號是分子 後面的小括號是分母
題目要問這個分式的最大值和最小值
5.想法：
我令sinx+cosx=t => sinx*cosx=(t^2-1)/2
f(x)=(t^2-1)/(2+2t)
然後我令y=(t^2-1)/(2+2t)
化簡後得到t^2-2yt-(2y+1)=0
因為t是實數
所以上面的方程式有實跟
=> (2y)^2+4(2y+1)>=0
展開後得4y^2+8y+4>=0
y^2+2y+1>=0
(y+1)^2>=0
所以y屬於R
這樣不就表示原式不存在最大值跟最小值?
可是答案給最大值為[(根號2)-1]/2
最小值為-[(根號2)+1]/2
看了半天看不出來我哪裡算錯或是推倒有誤
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◆ From: 61.229.148.188
※ 編輯: ALiu 來自: 61.229.148.188 (10/04 01:30)
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