\[x\]	
\[f(x)\]
\[-5\]	
\[0\]
\[-4\]	
\[2\]
\[-3\]	
\[6\]
\[-2\]	
\[7\]
\[-1\]	
\[5\]
\[0\]	
\[3\]
\[1\]	
\[0\]
\[2\]	
\[-3\]
\[3\]	
\[-5\]
\[4\]	
\[-1\]
\[5\]	
\[2\]
Qual é a taxa de variação média de 
\[f\] sobre o intervalo 
\[[3,4]\]?
Não arredonde sua resposta.


Para calcular a taxa de variação média de \( f(x) \) sobre o intervalo \([3, 4]\), utilizamos a fórmula:

\[
\text{Taxa de variação média} = \frac{f(b) - f(a)}{b - a}
\]

Neste caso, temos \( a = 3 \) e \( b = 4 \).

Usando os valores dados:

- \( f(3) = -5 \)
- \( f(4) = -1 \)

Substituindo na fórmula:

\[
\text{Taxa de variação média} = \frac{f(4) - f(3)}{4 - 3} = \frac{-1 - (-5)}{1} = \frac{-1 + 5}{1} = \frac{4}{1} = 4
\]

Portanto, a taxa de variação média de \( f(x) \) sobre o intervalo \([3, 4]\) é \(4\).

Would you like more details or have any questions? Here are some related questions to explore:

1. How would the rate of change be affected if the interval were expanded to \([2, 4]\)?
2. What does it mean if the average rate of change is negative?
3. How does the average rate of change relate to the behavior of the function between \(x = 3\) and \(x = 4\)?
4. Can the average rate of change be zero over an interval? What would that imply?
5. How is the average rate of change connected to the concept of a secant line?
6. If the function were linear, how would the average rate of change differ across intervals?
7. How does the average rate of change help in understanding the overall trend of the function?
8. How would the rate of change vary if calculated over a larger interval like \([-5, 5]\)?

**Tip:** The average rate of change is a powerful tool for understanding how a function behaves over an interval, particularly when the function is not linear.

Learn how to calculate the average rate of change of a function over the interval [3, 4] using the formula. Detailed step-by-step solution provided with function evaluations. Suitable for advanced high school students in Grades 11-12.

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