Questions: What is the average rate of change of g over the interval [-2,4] ?

Find the average rate of change of \( g(x) = -\frac{x^{2}}{4} + 7 \) over the interval \([-2, 4]\).

Calculate \( g(-2) \).

\[ g(-2) = -\frac{(-2)^{2}}{4} + 7 = -\frac{4}{4} + 7 = -1 + 7 = 6 \]

Calculate \( g(4) \).

\[ g(4) = -\frac{(4)^{2}}{4} + 7 = -\frac{16}{4} + 7 = -4 + 7 = 3 \]

Compute the average rate of change.

The average rate of change is given by: \[ \text{Average rate of change} = \frac{g(4) - g(-2)}{4 - (-2)} = \frac{3 - 6}{4 - (-2)} = \frac{-3}{6} = -0.5 \]

The average rate of change of \( g(x) \) over the interval \([-2, 4]\) is \(\boxed{-0.5}\).

The average rate of change of \( g(x) \) over the interval \([-2, 4]\) is \(\boxed{-0.5}\).