Question

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

Answer 1

The given function is f(x) = sinx − ax + b.

f(x) = sinx − ax + b

Differentiating both sides with respect to x, we get

$f\text{'}\left(x\right)=\cos x-a$

It is given that, f(x) increases on R.

$\therefore f\text{'}\left(x\right)\ge 0$ ∀ x ∈ R

$\Rightarrow \cos x-a\ge 0$ ∀ x ∈ R

$\Rightarrow a\le \cos x$ ∀ x ∈ R

$\Rightarrow a\le -1\left[-1\le \cos x\le 1\right]$

∴ a ∈ (−∞, −1]

Thus, the values of 'a' for which the function f(x) = sin x − ax + b increases on R are (−∞, −1].


The values of 'a' for which the function f(x) = sin x − ax + b increases on R are ___(−∞, −1]___.