Question

The function \( f(x) = \sin x - kx - c \), where \( k \) and \( c \) are constants, decreases always when

• A. \( k>1 \)
• B. \( k \le 1 \)
• C. \( k<1 \)
• D. \( k \le 0 \)

Hint:

For a function to decrease, its derivative must be less than or equal to zero.

Answer 1

The Correct Option is B

Step 1: Differentiate the function.
The derivative of \( f(x) = \sin x - kx - c \) is \( f'(x) = \cos x - k \). For the function to decrease, we need \( f'(x) \leq 0 \), which holds when \( k \leq 1 \).
Step 2: Conclusion.
Thus, the function decreases when \( k \le 1 \).
Final Answer: \[ \boxed{k \le 1} \]