find the average rate of change on the interval specified for real number m in simplest form. g(x) = -6x + 5…
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
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
[ \begin{align*} \frac{g(5 + m)-g(5)}{(5 + m)-5}&=\frac{(-25-6m)-(-25)}{m}\ &=\frac{-25-6m + 25}{m}\ &=\frac{-6m}{m} \end{align*} ]
Answer:
(-6)