Finding the average rate of change of a function Find the average rate of change of \( g(x)=3 x^{2}-2 x \) from \( x=-4 \) to \( x=-2 \). Simplify your answer as much as possible. \( \square \)

To find the **average rate of change** of the function \( g(x) = 3x^{2} - 2x \) from \( x = -4 \) to \( x = -2 \), we use the formula: \[ \text{Average Rate of Change} = \frac{g(b) - g(a)}{b - a} \] where \( a = -4 \) and \( b = -2 \). 1. **Calculate \( g(-4) \):** \[ g(-4) = 3(-4)^2 - 2(-4) = 3(16) + 8 = 48 + 8 = 56 \] 2. **Calculate \( g(-2) \):** \[ g(-2) = 3(-2)^2 - 2(-2) = 3(4) + 4 = 12 + 4 = 16 \] 3. **Compute the average rate of change:** \[ \text{Average Rate of Change} = \frac{16 - 56}{-2 - (-4)} = \frac{-40}{2} = -20 \] So, the average rate of change of \( g(x) \) from \( x = -4 \) to \( x = -2 \) is: \[ \boxed{-20} \]