Prove that there is ONLY one real root on the interval of (0

来源：学生作业帮编辑：大师作文网作业帮分类：数学作业时间：2024/11/13 10:11:10

Prove that there is ONLY one real root on the interval of (0,1) for the equation x3-3x2+6x=1

x³-3x²+6x-1=0
设 f(x) = x³-3x²+6x-1；
求导得：f '(x) = 3x² - 6x+6,
3x² - 6x+6=0
x²-2x+2=0
(x-1)²=0.
f '(x)=0 => x=1
因此(0,1)内,f '(x) > 0,所以：f(x) 在(0,1)上单调增加,
因为：f(0)=-1；f(1)=3；
故 f(x) 在(0,1)上至多只有一个零值点.
即证方程 x³-3x²+6x-1=0在区间(0,1)内只有一个实根.

There is only an interval of three days. He is the only one of the students that have been there. There is only one cover of plants on Earth翻译 At the root of volunteering is the idea that one person may There is only one book on the desk反义疑问句 there is only one sheep on the farm.对only one提问 There is only one glass on the table.对only one提问 There is only one map on the wall.（only one划线）对话线部分提问 there is only one candle on the cake对only one提问 there is only one cup on the table,only one画线对划线部分提问 There is only one box on the table对only one提问现在就要 there is only one sheep on the farm.对only one提问 How many she