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Show that f(x) = x – sin x is increasing for all x ϵ R. |
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Answer» Given as f(x) = x – sin x f'(x) = (d/dx)(x - sin x) ⇒ f’(x) = 1 – cos x As given x ϵ R ⇒ –1 < cos x < 1 ⇒ –1 > cos x > 0 ⇒ f’(x) > 0 Thus, condition for f(x) to be increasing Hence, f(x) is increasing on interval x ∈ R |
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