over which interval does function f increase the fastest? f(x) -4, -2 0, 6 -10, -4 -2, 0
over which interval does function f increase the fastest? f(x) -4, -2 0, 6 -10, -4 -2, 0
Answer
Explanation:
Step1: Recall rate - of - change concept
The rate of increase of a function on an interval is given by the average rate of change $\frac{f(b)-f(a)}{b - a}$. Visually, it is related to the steepness of the graph on the interval.
Step2: Analyze each interval
- For $[-4,-2]$: The graph has a relatively steep upward - slope.
- For $[0,6]$: The slope is positive but less steep compared to some other intervals.
- For $[-10,-4]$: The function is increasing but the slope is less steep than in $[-4,-2]$.
- For $[-2,0]$: The slope is positive but not as steep as in $[-4,-2]$.
Answer:
A. $[-4, -2]$