UPSC NDA I 2021 Mathematics Solved Paper

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)=sin‌x
∴f′(x)=cos‌x
For x∈(0,‌

π

2

),cos‌x>0 and for x∈(‌

π

2

,π),cos‌x<0
∴ For x∈(0,π),f(x) increases to max at ‌

π

2

and then decreases to min at π.
For x∈(‌

5π

2

,3π)‌‌,cos‌x<0
∴f(x) decreases for x∈(‌

5π

2

,3π)
Statement 1 is false and statement 2 is correct