Question

average rate of change from a graph
to find the average rate of change from a graph, we simply identify the two coordinates
(x₁,y₁) and (x₂,y₂) we need and find the slope.
example: find the average rate of change of f(x) on the interval 2 ≤ x ≤ 5

Explanation:

Step1: Identify endpoints

Find \( (x_1, y_1) \) at \( x = 2 \) and \( (x_2, y_2) \) at \( x = 5 \) from the graph. Assume \( (2, 3) \) and \( (5, 6) \) (approximate from graph).

Step2: Apply average rate formula

Use \( \text{Average Rate of Change} = \frac{f(x_2) - f(x_1)}{x_2 - x_1} \). Substitute \( x_1 = 2, y_1 = 3, x_2 = 5, y_2 = 6 \).

$$ \frac{6 - 3}{5 - 2} = \frac{3}{3} = 1 $$

Answer:

The average rate of change of \( f(x) \) on \( 2 \leq x \leq 5 \) is \( 1 \) (values depend on exact graph coordinates, this is a sample calculation).