Monotonicity

f(x)=x^(5)-20x^(3)+240x, then f(x) is O Monotonically decreasing everywhere O Monotonically decreasing on (0,oo) O Monotonically increasing on (-oo,0) O Monotonically increasing everywhere

If g(x) is monotonically increasing and f(x) is monotonically decreasing for x R and if (gof) (x) is defined for x e R, then prove that (gof)(x) will be monotonically decreasing function. Hence prove that (gof) (x +1)leq (gof) (x-1).

The function f(x)= (x^(2))/(e^(x)) monotonically increasing if

For each of the following graph comment on monotonically of f(x) " at" x=a

The function f(x)=cos x -2 px is monotonically decreasing for

f(x)=4tanx-tan^2x+tan^3x ,x!=npi+pi/2, (a)is monotonically increasing (b)is monotonically decreasing (c)has a point of maxima (d)has a point of minima

Interval in which the function f(x)=log_((1)/(2))(x^(2)-2x-8) is monotonically increasing,is