Question

to find the average rate of change from a table, we simply identify the two coordinates (x₁, y₁), (x₂, y₂), and find the slope. example: find the average rate of change of f(x) on the interval -3 ≤ x ≤ 6. the table has x values: -3, -1, 3, 6, 7 and corresponding f(x) values: -3, 1, 9, 15, 17.

Explanation:

Step1: Identify endpoints

For interval \(-3 \leq x \leq 6\), find \(f(-3)\) and \(f(6)\) from table.
\(f(-3) = -3\), \(f(6) = 15\).

Step2: Apply average rate formula

Average rate of change formula: \(\frac{f(b) - f(a)}{b - a}\), where \(a = -3\), \(b = 6\).
Substitute values: \(\frac{15 - (-3)}{6 - (-3)} = \frac{18}{9} = 2\).

Answer:

The average rate of change of \(f(x)\) on \(-3 \leq x \leq 6\) is \(2\).