AP Precalculus - Average Rate of Change

**Formula:** f(b) - f(a) / (b - a)

**Key Points:**

The formula calculates the average rate of change of a function over a given interval.

The difference in function values (F(b) - F(a)) is divided by the difference in input values (b - a).

**Example 1:**

**Function**: f(x) = 3x^2**Interval**: [1, 3] [a, b] a = 1, b = 3**Average Rate of Change**= (F(3) - F(1)) / (3 - 1)**Substituting into the function:**(27 - 3) / 2 = 24 / 2 = 12

**In Example 1,** **the function f(x) = 3x^2** **has an** **average rate of change of 12** **over** **the** **interval [1, 3].**

**Example 2:**

**Function**: f(x) = x^2 + 2**Interval**: [2, 4] [a, b] a = 2, b = 4**Average Rate of Change**= (F(4) - F(2)) / (4 - 2)**Substituting into the function**: (18 - 6) / 2 = 12 / 2 = 6

**In Example 2,** **the function f(x) = x^2 + 2** **has an** **average rate of change of 6** **over** **the** **interval [2, 4].**

**Conclusion:**

Overall, the Average rate of change provides insight into the trend of the function within the specified interval.

# AP Precalculus - Average Rate of Change

**Formula:** f(b) - f(a) / (b - a)

**Key Points:**

The formula calculates the average rate of change of a function over a given interval.

The difference in function values (F(b) - F(a)) is divided by the difference in input values (b - a).

**Example 1:**

**Function**: f(x) = 3x^2**Interval**: [1, 3] [a, b] a = 1, b = 3**Average Rate of Change**= (F(3) - F(1)) / (3 - 1)**Substituting into the function:**(27 - 3) / 2 = 24 / 2 = 12

**In Example 1,** **the function f(x) = 3x^2** **has an** **average rate of change of 12** **over** **the** **interval [1, 3].**

**Example 2:**

**Function**: f(x) = x^2 + 2**Interval**: [2, 4] [a, b] a = 2, b = 4**Average Rate of Change**= (F(4) - F(2)) / (4 - 2)**Substituting into the function**: (18 - 6) / 2 = 12 / 2 = 6

**In Example 2,** **the function f(x) = x^2 + 2** **has an** **average rate of change of 6** **over** **the** **interval [2, 4].**

**Conclusion:**

Overall, the Average rate of change provides insight into the trend of the function within the specified interval.