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If f(x) = sinx - x/2 is increasing function, then (A) 0 < x < π/3

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in Limit, continuity and differentiability by (41.7k points)

 If f(x) = sinx - x/2 is  increasing function, then

(A) 0 < x < π/3

(B) - π/3 < x < 0

(C) - π/3 < x < π/3

(D) x = π/2 

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1 Answer

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Answer is (C) - π/3 < x < π/3

We have

f(x) = sinx - x/2 ⇒ f'(x) = cosx - 1/2

We know that f'(x) > 0 for increasing function. Obviously, it is increasing for

- π/3 < x < π/3

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