the function $y = f(x)$ is graphed below. what is the average rate of change of the function $f(x)$ on the…
the function $y = f(x)$ is graphed below. what is the average rate of change of the function $f(x)$ on the interval $4 \\leq x \\leq 5$?
Answer
Explanation:
Step1: Recall the formula for average rate of change
The average rate of change of a function (y = f(x)) on the interval ([a,b]) is given by (\frac{f(b)-f(a)}{b - a}). Here, (a = 4) and (b=5).
Step2: Find (f(4)) and (f(5)) from the graph
From the graph, when (x = 4), (f(4)=0); when (x = 5), (f(5)=- 6).
Step3: Substitute into the formula
Substitute (a = 4), (b = 5), (f(4)=0) and (f(5)=-6) into (\frac{f(b)-f(a)}{b - a}). We get (\frac{f(5)-f(4)}{5 - 4}=\frac{-6-0}{5 - 4}).
Step4: Simplify the expression
(\frac{-6-0}{5 - 4}=\frac{-6}{1}=-6)
Answer:
(-6)