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

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

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)=-2x^(3)-9x^(2)-12x+1

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

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

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 range of the function f(x)=1+sinx+sin^(3)x+sin^(5)x+…… when x in (-pi//2,pi//2) , is

Investigate the behaviour of the following functions for monotonicity in the given intervals. (i) f(x) = -sin^(3)x + 3sin ^(2)x +5, x epsilon [-pi/2, pi/2] . (ii) f(x) = secx - cosec x, x epsilon (0, pi/2) .