Find the set of all values of the parameter 'a' for which the function, `f(x) = sin 2x - 8(a + 1)sin x + (4a^2 + 8a - 14)x` increases for all `x in R` and has no critical points for all `a in R.`

Find the set of all values of the parameter 'a' for which the function, f(x) = sin 2x - 8(a + b)sin x + (4a^2 + 8a - 14)x increases for all x in R and has no critical points for all a in R.

if has set of all values of the parameter 'a' for which the function f(x) = sin 2x -8 (a+1) sin x + (4a^(2) +8a -14) x increases for all x in R and has no critical points for all x in R" is " (-oo , -m -sqrt(n))uu (sqrt(n) ,oo) then (m^(2) +n^(2)) is (where m,n are prime numbers):

Find all the values of the parameter'a' for which the function; f(x)=8ax-a sin6x-7x-sin5x increases & has no critical points for all x in R

Find all the values of the parameter'a' for which the function; f(x)=8ax-a sin 6x-7x-sin 5x increases & has no critical points for all x in R .

Find all possible values of the parameter ' b ' for which the function, f(x)=sin 2x-8(b+2)cos x - (4b^(2)+16b+6)x is monotonic decreasing throughout the number line and has no critical points.

Write the set of values of a for which the function f(x)=a x+b is decreasing for all x in R .

Find the values of ' a ' for which the function f(x)=sin x-ax+4 is increasing function on R.

The set of all values of a for which the function f(x)=((a^2-1)/3)x^3+(a-1)x^2+2x+1 increases on R, is