函数f(x)=x^4-4x^3+ax^2-1在区间[0,1]上单调递增,在区间[1,2]上单调递减.1 求a的值 2.求在区间[-2.2]上fx的最大值和最小值
人气:380 ℃ 时间:2019-10-19 20:11:59
解答
1)f'(x)=4x^3-12x²+2ax
由题意,x=1为极大值点
故f'(1)=4-12+2a=0
得:a=4
2)f'(x)=4x^3-12x²+8x=4x(x²-3x+2)=4x(x-1)(x-2)
得极值点分别为0,1,2
f(x)=x^4-4x^3+4x²-1
f(0)=-1为极小值
f(1)=1-4+4-1=0为极大值
f(2)=16-32+16-1=-1为极小值
端点值:f(-2)=16+32+16-1=63
比较得:在区间[-2,2],
最大值为f(-2)=63,最小值为f(0)=f(2)=-1
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