Question

find the average rate of change of the function $f(x)=sqrt{x}+1$ on the interval $4leq xleq9$. recall that the coordinates for the start of the interval are $(4,3)$. what are the coordinates for the end of the interval? what is the average rate of change for this function on the given interval?

Explanation:

Step1: Find function value at end - point

Given $f(x)=\sqrt{x}+1$, when $x = 9$, $f(9)=\sqrt{9}+1=3 + 1=4$. So the coordinates at the end of the interval are $(9,4)$.

Step2: Use average - rate - of - change formula

The average rate of change of a function $y = f(x)$ on the interval $[a,b]$ is $\frac{f(b)-f(a)}{b - a}$. Here, $a = 4$, $b = 9$, $f(4)=\sqrt{4}+1=3$, $f(9)=4$. Then $\frac{f(9)-f(4)}{9 - 4}=\frac{4 - 3}{5}=\frac{1}{5}$.

Answer:

Coordinates at end of interval: $(9,4)$
Average rate of change: $\frac{1}{5}$