For what values of a does the curve `f(x)=x(a^2-2a-2)+cosx` is always strictly monotonic decreasing `AA x in R`

f(x) = sin x is a strictly decreasing in (pi/2,pi)

Show that the function f(x)=(3x+5)/(x+2) is strictly monotonic increasing in [0, oo) .

For what values of x , the function f(x)=x+ (4)/(x^(2)) is monotonically decreasing

The least integral value of x where f(x)=log_((1)/(2))(x^(2)-2x-3) is monotonically decreasing is

The number of integral values of a for which f(x) = x^3 + (a + 2)x^2 + 3ax + 5 is monotonic in AA x in R

For what values of a , does the function f(x)=((sqrt(a+5))/(1-a)-1)x^3-2x+ln(3/2) decreases (not strictly) on

Write the set of values of a for which f(x)=cosx+a^2\ x+b is strictly increasing on R .

Show that the function f(x)=x^(2) is neither strictly increasing nor strictly decreasing on R

Show that the function f(x)=x^(2) is neither strictly increasing nor strictly decreasing on R

Let set of all possible values of lamda such that f (x)= e ^(2x) - (lamda+1) e ^(x) +2x is monotonically increasing for AA x in R is (-oo, k]. Find the value of k.