To determine which statement accurately describes the average rate of change for the function \( f(x) \) on the specified intervals, we need to analyze the graph of \( f(x) \).
The average rate of change of a function on an interval \([a, b]\) is calculated using the formula:
\[ \text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a} \]
In graphical terms, this represents the slope of the secant line connecting the points \((a, f(a))\) and \((b, f(b))\) on the curve.
Here are the statements you provided:
- The average rate of change is negative on the interval \([0,1]\) and on the interval \([3,4]\).
- The average rate of change is negative on the interval \([1,3]\) and also on the interval \([6,7]\).
- The average rate of change is negative only on the interval \([1,3]\).
- The average rate of change is negative only on the interval \([6,7]\).
To conclude which statement is correct, examine the graph:
- If the graph decreases from \(x=0\) to \(x=1\), then the first part of statement 1 is correct.
- If the graph increases from \(x=1\) to \(x=3\) (since the rate of change would be positive), then statement 2 would not be correct, and neither would statement 3.
- Lastly, if the graph shows a downward trend from \(x=6\) to \(x=7\), that would support statement 2, and part of statement 1 might not hold.
After analyzing the graph for these behaviors, you would select the appropriate statement based on the observed trends. Without the actual visual graph to reference, make the decision based on the slopes of the secant lines indicated on the specified intervals.
Please confirm your observations against the graph to find the most accurate response!
1 answer