Question

find the average rate of change on the interval specified for real number m in simplest form. g(x) = -6x + 5 on 5, 5 + m answer

Explanation:

Step1: Recall the formula for average rate of change

The average rate of change of a function \(y = g(x)\) on the interval \([a,b]\) is \(\frac{g(b)-g(a)}{b - a}\). Here, \(a = 5\) and \(b=5 + m\).

Step2: Find \(g(5)\) and \(g(5 + m)\)

• Substitute \(x = 5\) into \(g(x)=-6x + 5\): \(g(5)=-6\times5+5=-30 + 5=-25\).
• Substitute \(x = 5 + m\) into \(g(x)=-6x + 5\): \(g(5 + m)=-6(5 + m)+5=-30-6m + 5=-25-6m\).

Step3: Calculate the average rate of change

$$
LATEXBLOCK0
$$

Answer:

\(-6\)