Question

Average rate of change I5Find the average rate of change of g(x)=(-16/x) over the interval -13,-10.

Answer 1

The average rate of change of g(x) = -16/x over the interval -13 to -10 is 8/65.

Step-by-step explanation:

The average rate of change of a function is the change in the output (y-values) divided by the change in the input (x-values) over a specified interval. In this case, we are given the function g(x) = -16/x and the interval -13 to -10.

To find the average rate of change, we need to calculate the change in output and the change in input. Let's start with the change in output:

1. Plug the starting value of the interval into the function: g(-13) = -16/(-13) = 16/13.
2. Plug the ending value of the interval into the function: g(-10) = -16/(-10) = 8/5.
3. Calculate the change in output: (8/5) - (16/13).
4. Simplify the expression: (8/5) - (16/13) = (104/65) - (80/65) = 24/65.

Next, let's find the change in input:

1. Calculate the change in input: -10 - (-13) = -10 + 13 = 3.

Now, we can calculate the average rate of change:

1. Divide the change in output by the change in input: (24/65) / 3.
2. Divide the numerator by the denominator: (24/65) ÷ 3 = (24/65) * (1/3) = 8/65.

Therefore, the average rate of change of g(x) = -16/x over the interval -13 to -10 is 8/65.