数学题第二小题不会啊,请求高手指导
(I)
(1)x>=2
f(x)=x^3+2ax^2-4ax+1
令f'(x)=3x^2+4ax-4a>=0
i)-2a/3= -3
f'(2)=12+4a>=0,a>=-3
a>=-3
ii)-2a/3>2,a=-3
(2)x2,a>3
f'(2)=12-4a>=0,a=2
f(m)=m^3+2am^2-4am+1=6m+1
m^2+2am-4a=6
f'(m)=3m^2+4am-4a=6
3m^2+4am-4a=m^2+2am-4a
2m^2+2am=0,m= -a
而a>=0,无解
(2)m<2
f(m)=m^3-2am^2+4am+1=6m+1
m(m^2-2am+4a-6)=0
...全部
(I)
(1)x>=2
f(x)=x^3+2ax^2-4ax+1
令f'(x)=3x^2+4ax-4a>=0
i)-2a/3= -3
f'(2)=12+4a>=0,a>=-3
a>=-3
ii)-2a/3>2,a=-3
(2)x2,a>3
f'(2)=12-4a>=0,a=2
f(m)=m^3+2am^2-4am+1=6m+1
m^2+2am-4a=6
f'(m)=3m^2+4am-4a=6
3m^2+4am-4a=m^2+2am-4a
2m^2+2am=0,m= -a
而a>=0,无解
(2)m<2
f(m)=m^3-2am^2+4am+1=6m+1
m(m^2-2am+4a-6)=0
i)m=0,
f'(m)=3m^2-4am+4a=4a=6,a=3/2
ii)m≠0
m^2-2am+4a-6=0。
。。。。。。。。。。。(1)
f'(m)=3m^2-4am+4a=6。。。。。。。
(2)
(2)-(1)
2m^2-2am=0
m=a,代入(1)
m^2-2m^2+4m-6=0,m^2-4m+6=0,无解
综上,a=3/2
f(x)=x^3+3x|x-2|+1。收起
