For the function f(x)= 8/x+7,find the average rate of change of f from 1 to x.

Did you mean

f(x) = 8/(x+7)

then f(1) = 8/8 = 1

avg rate of change = (f(x) - f(1) )/(x-1)
= (8/(x+7) - 1)/(x-1)
= ( (8 - x - 7)/(x+7) )/(x-1)
= ( (1-x)/x+7) )/(x-1)
= -1/(x+7)

thank you so much!!

You are welcome.

(I have just answered 13 questions this morning, and you are the only one to say thank you or acknowledge the answer, much appreciated)

Well, if I calculate the average rate of change of f from 1 to x for the given function, it might take a while. But don't worry, I've got a joke to pass the time:

Why did the scarecrow win an award?
Because he was outstanding in his field!

Okay, now back to your question. To find the average rate of change of f from 1 to x, we need to find the slope of the line connecting the two points (1, f(1)) and (x, f(x)). So let's get calculating!

The value of f(1) is:
f(1) = 8/1 + 7 = 8 + 7 = 15

The value of f(x) is:
f(x) = 8/x + 7

Now, let's find the slope of the line between these two points using the formula:
slope = (f(x) - f(1))/(x - 1)

slope = (8/x + 7 - 15)/(x - 1)

slope = (8/x + 7 - 15)/(x - 1)

And there you have it! That's how you can find the average rate of change of f from 1 to x. I hope this helps and that my joke kept you entertained!

To find the average rate of change of a function from 1 to x, we need to calculate the difference in the function values at those two points and divide it by the difference in the inputs.

Given the function f(x) = 8/x+7, we need to substitute x = 1 and x = x into the function to find the corresponding function values.

First, let's find f(1):
f(1) = 8/1 + 7 = 8 + 7 = 15

Next, let's find f(x):
f(x) = 8/x + 7

Now, we can find the average rate of change by subtracting f(1) from f(x) and then dividing it by the difference in the inputs, which is x - 1:

Average Rate of Change = (f(x) - f(1))/(x - 1)

Plugging in the values:
Average Rate of Change = ((8/x + 7) - 15)/(x - 1)

Simplifying the expression further would depend on the specific value of x you want to calculate the average rate of change at.