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

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

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

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)=(log_(e)x)^(2)+(log_(e)x)

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)

Determine the intervals of monotonicity for the following functions : f(x) = 2x^(3) -9x^(2) -24x +7 ,