**Question:** True or false: If \( f(x) = 12 \) for all real numbers \( x \), then \( f''(x) = 0 \) for all real numbers \( x \). **Analysis:** In this question, we are asked to determine whether the statement is true or false. Let's analyze: 1. \( f(x) = 12 \) represents a constant function where the value of the function is the same (12) for all values of \( x \). 2. The first derivative of a constant function, \( f'(x) \), is 0 because the rate of change of a constant is zero. 3. The second derivative, \( f''(x) \), is also 0 because the derivative of 0 is 0. Therefore, the statement is **true**. If \( f(x) \) is constant, then its second derivative \( f''(x) \) is indeed 0 for all \( x \).

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