If f(x)`=sin x-a sin 2x-(1)/(3) sin 3x+2ax` is an increasing function for all real values of x, show that, `a gt 1`.

If f(x)= x^(3) + ax^(2) + bx + c is an increasing function for all real values of x then-

If f(x) =x^(3) +ax^(2)+bx +5 sin^(2) x is an increasing function on R, then

If the function f(x)=(a sin x+2 cos x)/(sin x + cos x) is strictly increasing for all values of x, then a gt k , find k.

If the function f(x) = (K sin x + 2 cos x)/(sin x + cos x) is strictly increasing for all values of x, then

If the function f(x)=(K sin x+2cos x)/(sin x+cos x) is strictly increasing for all values of x, then K 1K 2

Let f(x) be a function such that f(x)=log_((1)/(3))(log_(3)(sin x+a)). If f(x) is decreasing for all real values of x, then

Let f(x) be a function such that f'(x)=log_(1/3) [log_(3)(sin x+a)] . If f(x) is decreasing for all real values of x then a gt k , find k.

If f(x)=x^(3)+ax^(2)+bx+5sin^(2)x, AA x in R is an increasing function, then …………..