Separate the intervals of monotonocity for the function `f(x)=x^2e^(-x)`

Separate the intervals of monotonocity for the function f(x)=-2x^(3)-9x^(2)-12x+1

Separate the intervals of monotonocity for the function f(x)=(log_(e)x)^(2)+(log_(e)x)

Separate the intervals of monotonocity of the function: f(x)=3x^(4)-8x^(3)-6x^(2)+24x+7

Separate the intervals of monotonocity for the function f(x)=3cos^(4)x+10cos^(3)x+6cos^(2)x-3,x in[0,pi]

Separate the intervals of monotonocity for the function f(x)=sin x+cos x,x in(0,2 pi)

Separate the intervals of monotonocity of the function: f(x)=-sin^(3)x+3sin^(2)x+5,x in[-(pi)/(2),(pi)/(2)]

Find the interval of monotonocity of the function f(x)=(|x-1|)/(x^(2))

Separate the intervals of monotonocity of the following function: (i) f(x)=3x^(4)-8x^(3)-6x^(2)+24x+7 (ii) F(x) =-sin^(3)x+3sin^(2)x+5,x "in" (-pi//2,pi//2) (iii) f(x)=(2^(x)-1)(2^(x)-2)^(2)

The interval of monotonicity of the function f(x)=(x)/(log_(e)x), is