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  2. AP Pre Calculus
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How do you calculate the average rate of change of f(x)f(x)f(x) over [a,b][a, b][a,b]?

  1. Find f(a)f(a)f(a) and f(b)f(b)f(b). 2. Calculate f(b)−f(a)f(b) - f(a)f(b)−f(a). 3. Calculate b−ab - ab−a. 4. Divide (f(b)−f(a))(f(b) - f(a))(f(b)−f(a)) by (b−a)(b - a)(b−a).
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How do you calculate the average rate of change of f(x)f(x)f(x) over [a,b][a, b][a,b]?

  1. Find f(a)f(a)f(a) and f(b)f(b)f(b). 2. Calculate f(b)−f(a)f(b) - f(a)f(b)−f(a). 3. Calculate b−ab - ab−a. 4. Divide (f(b)−f(a))(f(b) - f(a))(f(b)−f(a)) by (b−a)(b - a)(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.

What is the formula for average rate of change over the interval [a, b]?

f(b)−f(a)b−a\frac{f(b) - f(a)}{b - a}b−af(b)−f(a)​

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.