设函数f(x)=2x3-3(a-1)x2+1其中a大于等于1.(1)求f(x)的单调区间还有第二问:讨论的f(x)极值
来源:学生作业帮助网 编辑:作业帮 时间:2024/08/01 06:47:30
![设函数f(x)=2x3-3(a-1)x2+1其中a大于等于1.(1)求f(x)的单调区间还有第二问:讨论的f(x)极值](/uploads/image/z/3783816-0-6.jpg?t=%E8%AE%BE%E5%87%BD%E6%95%B0f%28x%29%3D2x3-3%28a-1%29x2%2B1%E5%85%B6%E4%B8%ADa%E5%A4%A7%E4%BA%8E%E7%AD%89%E4%BA%8E1.%281%29%E6%B1%82f%28x%29%E7%9A%84%E5%8D%95%E8%B0%83%E5%8C%BA%E9%97%B4%E8%BF%98%E6%9C%89%E7%AC%AC%E4%BA%8C%E9%97%AE%EF%BC%9A%E8%AE%A8%E8%AE%BA%E7%9A%84f%28x%29%E6%9E%81%E5%80%BC)
xŒJ0dž`/"aGzqc-NQ2E6&
Z]FtI)
/?|?~ 5VKAjYUQB)l9|Mdr(h9gt|D[oWɵˆ8l- :ip!th#2w?~lju;#9 7P!UC
"\o!:AX\\ݾs\"]7/E:wGO"i@H_ѦWXP(Ŀ]{.' nzƳ O[J"
D,˧K#6+wUms
设函数f(x)=2x3-3(a-1)x2+1其中a大于等于1.(1)求f(x)的单调区间还有第二问:讨论的f(x)极值
设函数f(x)=2x3-3(a-1)x2+1其中a大于等于1.(1)求f(x)的单调区间
还有第二问:讨论的f(x)极值
设函数f(x)=2x3-3(a-1)x2+1其中a大于等于1.(1)求f(x)的单调区间还有第二问:讨论的f(x)极值
1
f(x)=2x3-3(a-1)x2+1
f'(x)=6x^2-6(a-1)x=6x[x-(a-1)]
f'(x)=0==>x1=0,x2=a-1
a=1,f'(x)=6x^2≥0,总成立
f(x)单调增区间(-∞,+∞)
a>1,
f(x)单调增区间(-∞,0),(a-1,+∞)
f(x)单调减区间(0,a-1)
2
a=1,f(x)无极值
a>1,由(1)可知
f(x)极大值为f(0)=1
f(x)极小值为f(a-1)=2(a-1)^3-3(a-1)^3+1=1-(a-1)^3