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How do you calculate the average rate of change of $f(x)$ over $[a, b]$?
1. Find $f(a)$ and $f(b)$. 2. Calculate $f(b) - f(a)$. 3. Calculate $b - a$. 4. Divide $(f(b) - f(a))$ by $(b - a)$.
How do you determine if a function is increasing or decreasing?
1. Calculate the rate of change. 2. If the rate is positive, the function is increasing. 3. If the rate is negative, the function is decreasing.
Explain the concept of average rate of change.
Measures how much a function's output changes over a specific interval; the slope of the secant line.
What does a positive rate of change indicate?
That the function is increasing as the input increases.
What does a negative rate of change indicate?
That the function is decreasing as the input increases.
What is the average rate of change?
The change in a function's output divided by the change in its input over an interval.
Define positive rate of change.
Both quantities increase or decrease together.
Define negative rate of change.
As one quantity increases, the other decreases.