Prove that there is ONLY one real root on the interval of (0,1) for the equation x3-3x2+6x=1
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ProvethatthereisONLYonerealrootontheintervalof(0,1)fortheequationx3-3x2+6x=1ProvethatthereisONLYoner
Prove that there is ONLY one real root on the interval of (0,1) for the equation x3-3x2+6x=1
Prove that there is ONLY one real root on the interval of (0,1) for the equation x3-3x2+6x=1
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.
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Prove that there is ONLY one real root on the interval of (0,1) for the equation x3-3x2+6x=1
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