设函数f(x)=(1/3)x^3-ax^2-3a^2x+1(a>0).
来源:学生作业帮 编辑:搜搜做题作业网作业帮 分类:数学作业 时间:2024/07/08 22:47:17
设函数f(x)=(1/3)x^3-ax^2-3a^2x+1(a>0).
(1)求f'(x)的表达式
(2)求函数f(x)的单调区间、极大值和极小值
(1)求f'(x)的表达式
(2)求函数f(x)的单调区间、极大值和极小值
![设函数f(x)=(1/3)x^3-ax^2-3a^2x+1(a>0).](/uploads/image/z/17386347-3-7.jpg?t=%E8%AE%BE%E5%87%BD%E6%95%B0f%28x%29%3D%281%2F3%29x%5E3-ax%5E2-3a%5E2x%2B1%28a%3E0%29.)
f'(x)=x²-2ax-3a²=(x-3a)(x+a)
令f'(x)=(x-3a)(x+a)=0
得x1=3a,x2=-a
当3a≤x , f'(x)>0 ,f(x)在[3a,+∝)为单调增加
当-a≤x≤3a ,f'(x)
令f'(x)=(x-3a)(x+a)=0
得x1=3a,x2=-a
当3a≤x , f'(x)>0 ,f(x)在[3a,+∝)为单调增加
当-a≤x≤3a ,f'(x)
设函数f(x)=x^3+ax^2-9x-1(a
设函数f(x)=-1/3x^3+2ax^2+1/3a(0
设函数f(x)=x^3+ax^2-a^2x+1,g(x)=ax^2-2x+1,其中实数a不等0
设函数f(x)= -1/3x^3+2ax^2-3a^2x+a/3(0
设a>0,f(x)=1/3x^3-a/2x^2-ax+1
设函数f(x)=-1/3x~3+2ax~2-3a~2x+1(0
设函数f(x)=-1/3x^3+2ax^2-3a^2x+1(0
设函数f(x)=-1/3x^3+2ax^2-3a^2x+b,0
设函数f(x)=-1/3x^3+2ax^2-2a^2x+b,0
设函数f(x)=ax^2+bx+c((a≠0),满足f(x+1)=f(-x-3),且f(-2)>f(2),解不等式f(-
设函数f(x)=x^3+ax^2-a^2x+1,g(x)=ax^2-2x+1,其中实数a不等0,若a>0,求函数f(x)
设函数f(x)=1/3x^3-1/2ax^2-2a^2x+1(a