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 the set of all values of the parameter 'a' for which the function,f(x)=sin2x-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.

Find the smallest integer value of P for which the function f(x)=6Px-P sin4x-5x-sin3x is monotonic increasing and has no critical point on R

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.

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

The values of a for which the function f(x)=sin x - ax + b increases on R are …………..

Find the values of 'a' for which the function f(x)=sin x-a sin2x-(1)/(3)sin3x+2ax stricly increases throughout the number line.