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Show that f(x) = x – cos x is increasing for all x. |
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Answer» f(x) = x – cos x ∴ f'(x) = d/dx (x – cos x) = 1 – (-sin x) = 1 + sin x Now, -1 ≤ sin x ≤ 1 for all x ∈ R ∴ -1 + 1 ≤ 1 + sin x ≤ 1 for all x ∈ R ∴ 0 ≤ f'(x) ≤ 1 for all x ∈ R ∴ f'(x) ≥ 0 for all x ∈ R ∴ f is increasing for all x. |
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