`" The function "f(x)=(a+2)x^(3)-3ax^(2)+9ax-1" is always decreasing "AA x in R" .Then the range of "a" is "`

Find the values of a for which the function f(x)=(a+2)x^(3)-3ax^(2)+9ax-a decreasing for all real values of x.

The range of the function f(x)=9^(x)-3^(x)+1 is

The function f(x)=(tan^(-1)x)^(3)-(cot^(-1)x)^(2)+tan^(-1)x+2 is (a)decreasing AA x in R( b)increasing AA x in R (c)bounded (d) Many one functions

The function f(x)=2ax^(3)+3x^(2)+6(a-1)x+1 is decreasing for all real values of x .Then the greatest integral value of a is

The function f(x)=2ax^(3)+3x^(2)+6(a-1)x+1 is decreasing for all real values of x .Then the greatest integral value of a is

Range of the function f(x)=3^(x)+3^(x-2)+1 is

If the function f(x)=3 cos |x| -6 ax +b increases for all x in R then the range of value of a given by

Let f, g are differentiable function such that g(x)=f(x)-x is strictly increasing function, then the function F(x)=f(x)-x+x^(3) is (A) strictly increasing AA x in R (B) strictly decreasing AA x in R (C) strictly decreasing on (-oo,(1)/(sqrt(3))) and strictly increasing on ((1)/(sqrt(3)),oo) (D) strictly increasing on (-oo,(1)/(sqrt(3))) and strictly decreasing on ((1)/(sqrt(3)),oo)

If yR' is the least value of 'a' such that the function f(x) = x^(2) + ax +1 is increasing on [1, 2] and 'S' is the greatest value of ' a' such that the function f(x) = x^(2) + ax +1 is decreasing on [1, 2], then the value of |R — S| is_____________