The Total solution for NCERT class 6-12
Show that f(x) = x– sin x is increasing for all x ϵ R.
Given f (x) = x – sin x
⇒
⇒ f’(x)= 1 – cos x
Now, as given x ϵ R
⇒ –1< cos x < 1
⇒ –1> cos x > 0
⇒ f’(x)> 0
Hence, condition for f(x) to be increasing
Thus f(x) is increasing on interval x ∈ R