To find the average rate of change of the function \( h(x) = -x^2 - x + 19 \) on the interval \([-2, 1]\), we use the formula:
\[ \text{Average Rate of Change} = \frac{h(b) - h(a)}{b - a} \]
where \( a = -2 \) and \( b = 1 \).
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First, we need to calculate \( h(-2) \) and \( h(1) \).
\[ h(-2) = -(-2)^2 - (-2) + 19 = -4 + 2 + 19 = 17 \]
\[ h(1) = -(1)^2 - (1) + 19 = -1 - 1 + 19 = 17 \]
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Now, we can plug these values into the average rate of change formula:
\[ \text{Average Rate of Change} = \frac{h(1) - h(-2)}{1 - (-2)} = \frac{17 - 17}{1 + 2} = \frac{0}{3} = 0 \]
Therefore, the average rate of change of \( h(x) \) on the interval \([-2, 1]\) is \( 0 \).
The answer is \( 0 \).