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Consider the following statements in respect of the function f(x) = sin x:

1. f(x) increases in the interval (0, π).

2. f(x) decreases in the interval \(\left(\dfrac{5\pi}{2},3\pi\right).\)

Which of the above statements is/are correct?


1. 1 only
2. 2 only
3. Both 1 and 2
4. Neither 1 nor 2

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Best answer
Correct Answer - Option 2 : 2 only

Concept:

The function f(x):

  • Increases for the values x of having f'(x) > 0
  • Decreases for the values of x having f'(x) < 0

 

Calculation:

Given function is f(x) = sin x

∴ f'(x) = cos x

For x ∈ (0, \(π\over2\)), cos x > 0 and for x ∈ (\(π\over2\), π), cos x < 0

∴ For x ∈ (0, π), f(x) increases to max at \(π\over2\) and then decreases to min at π.

For x ∈ \(\left(\dfrac{5\pi}{2},3\pi\right)\), cos x < 0

∴ f(x) decreases for x ∈ \(\left(\dfrac{5\pi}{2},3\pi\right)\)

Statement 1 is false and statement 2 is correct

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