确定函数y=4x^3-6x^2-12x-10的单调区间

来源:学生作业帮助网 编辑:六六作业网 时间:2024/12/24 01:44:06
确定函数y=4x^3-6x^2-12x-10的单调区间确定函数y=4x^3-6x^2-12x-10的单调区间确定函数y=4x^3-6x^2-12x-10的单调区间y=4x^3-6x^2-12x-10y

确定函数y=4x^3-6x^2-12x-10的单调区间
确定函数y=4x^3-6x^2-12x-10的单调区间

确定函数y=4x^3-6x^2-12x-10的单调区间
y=4x^3-6x^2-12x-10
y'=12x²-12x-12
=12(x²-x-1)=0
x=(1+√5)/2

x=(1-√5)/2
所以
y‘>0时
x>(1+√5)/2或x<(1-√5)/2
即为单调增区间(-∞,(1-√5)/2),((1+√5)/2),+∞)
同理减区间为((1-√5)/2,(1+√5)/2)

y‘=12x^2-12x-12
y'=0
12x^2-12x-12=0
x^2-x-1=0
x=(1±√5)/2
x<(1-√5)/2 f'(x)>0 f(x)增
(1-√5)/2x>(1+√5)/2 f'(x)>0 f(x)增

y=4x^3-6x^2-12x-10
y'=12x^2-12x-12
令 y'=0
12x^2-12x-12=0
即x^2-x-1=0
x=(1±√5)/2
当 x<(1-√5)/2 时, y'>0 单调增
当 (1-√5)/2当x>(1+√5)/2 时, y'>0 单调增