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Show that f(x) = x – cos x is increasing for all x. - Mathematics and Statistics

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Question

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

Sum
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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

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Chapter 2.2: Applications of Derivatives - Very Short Answers

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SCERT Maharashtra Mathematics and Statistics (Arts and Science) [English] 12 Standard HSC
Chapter 2.2 Applications of Derivatives
Very Short Answers | Q 4

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