Question

Let
f(x) = root x/x+1
What is the average rate of change of f between x=3 and x = 10?

Answer 1

The average rate of change of f between x=3 and x=10 is (√10/11 - √3/4)/7.

Step-by-step explanation:

To find the average rate of change of f between x=3 and x=10, we need to calculate the difference in f(x) values at these two points and divide it by the difference in x-values. Let's start by finding f(3) and f(10).

First, substitute x=3 into the function: f(3) = √3/(3+1) = √3/4.

Next, substitute x=10 into the function: f(10) = √10/(10+1) = √10/11.

Now, we can find the average rate of change by subtracting f(3) from f(10) and dividing it by the difference in x-values: (f(10) - f(3))/(10-3) = (√10/11 - √3/4)/7.