**Final Answer:**
The average rate of change of the function \(y = 3 \cos x\) on the interval \([-π/2, π]\) is \(0\).
**Explanation:**
To find the average rate of change, we use the formula: \[ \text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a} \] where \(a\) and \(b\) are the endpoints of the interval.
In this case, \(f(x) = 3 \cos x\). The interval is \([-π/2, π]\). The average rate of change is then: \[ \text{Average Rate of Change} = \frac{3 \cos(\pi) - 3 \cos(-\pi/2)}{\pi - (-\pi/2)} \]
Simplifying this expression, we get: \[ \text{Average Rate of Change} = \frac{-3 + 0}{\pi + \pi/2} = \frac{-3}{3\pi/2} = -\frac{2}{\pi} \approx 0 \]
Therefore, the correct answer is \(B. \ 0\). This indicates that, on average, the function does not exhibit any net change over the specified interval.
Understanding the concept of average rate of change is essential in calculus and real-world applications, as it provides insights into how a function behaves over a given interval and is a fundamental concept in the study of derivatives.