Question
Download Solution PDFConsider 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?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
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 2 is correct Only.
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