设f(x)在x=0处连续,且lim(x趋于0)f(x)/x^2=1 ,证明函数f(x)在x=0处可导且取得极小值.
人气:348 ℃ 时间:2019-08-17 22:48:44
解答
f(x)在x=0处的导数为f‘(0)=lim(x趋于0)[f(x)-f(0)]/x因为f(x)在x=0连续,且lim(x趋于0)f(x)/x^2=1,所以f(0)=0lim(x趋于0)[f(x)-f(0)]/x=lim(x趋于0)f(x)/xlim(x趋于0)f(x)/x^2=1,说明f(x)在x=0处于x^2...可以利用洛必达法则直接写出一阶导和二阶导的值么?然后利用二阶导等于二,大于零直接写是极小值那你不是还要证明f(x)的二阶导存在嘛可是洛比达不可以直接写出fx的导数么?只能用导数定义?不行吧
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