Function `f(x)=cosx-2\ lambda\ x` is monotonic decreasing when (a) `lambda>1//2` (b) `lambda<1//2` (c) `lambda<2` (d) `lambda>2`

Explanation

To determine when the function \( f(x) = \cos x - 2\lambda x \) is monotonic decreasing, we need to analyze its derivative. A function is monotonic decreasing if its derivative is less than or equal to zero.

### Step-by-Step Solution:

1. **Find the Derivative**:
We start by finding the derivative of the function \( f(x) \).
\[
f'(x) = \frac{d}{dx}(\cos x - 2\lambda x) = -\sin x - 2\lambda
...