Maharashtra State BoardHSC Arts 12th Board Exam
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Show that f(x) = x – cos x is increasing for all x. - Mathematics and Statistics

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Sum

Show that f(x) = x – cos x is increasing for all x.

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Solution

f(x) = x – cos x

∴ f′(x) = 1 + sin x

Note that –1 ≤ sin x ≤ 1, ∀x

∴ –1 + 1 ≤ 1 + sin x ≤ 1 + 1, ∀x

∴ 0 ≤ 1 + sin x ≤ 2, ∀x

i.e., f′(x) ≥ 0 for all x.

Hence, f(x) is increasing for all x

Concept: Increasing and Decreasing Functions
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