If the function `f(x)=cos|x|-2a x+b` increases along the entire number scale, then (a) `a=b` (b) `a=1/2b` (c) `alt=-1/2` (d) `a >-3/2`

Explanation

To determine the conditions under which the function \( f(x) = \cos|x| - 2ax + b \) is increasing along the entire number scale, we need to analyze the derivative of the function.

### Step 1: Find the derivative of the function
The function is given as:
\[ f(x) = \cos|x| - 2ax + b \]

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