JAMIA 2024 — Mathematics PYQ
JAMIA | Mathematics | 2024The function f(x) = x + cos x is
Choose the correct answer:
- A.
always increasing
(Correct Answer) - B.
always decreasing
- C.
increasing for certain range of x
- D.
None of these
always increasing
Explanation
Mathematical Proof
The derivative we calculated is:
We know that the maximum value of sinx is 1. Therefore:
-
When sinx=1, f′(x)=1−1=0.
-
For all other values of x, \sin x < 1, which means 1 - \sin x > 0.
Since f′(x)≥0 for all real values of x, the function is always increasing.
Final Selection
The correct option is:
Always increasing (or Monotonically increasing).
Explanation
Mathematical Proof
The derivative we calculated is:
We know that the maximum value of sinx is 1. Therefore:
-
When sinx=1, f′(x)=1−1=0.
-
For all other values of x, \sin x < 1, which means 1 - \sin x > 0.
Since f′(x)≥0 for all real values of x, the function is always increasing.
Final Selection
The correct option is:
Always increasing (or Monotonically increasing).