Answer :

Given f (x) = sinx – ax + b


Now apply the derivative we get



Now applying the sum rule of differentiation and the differentiation of the constant term is 0 we get



Now applying the derivative, we get


f'(x)=cos x-a


Now given f(x) increases on R


f’(x)≥0 x


cos x-a≥0 x


cos x≥a x


This is possible when a≤-1


Hence a(-∞, -1]


The values of a for which the function f (x) = sinx – ax + b increases on R are (-∞, -1].


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