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9 ? For x ~ #/ 1 Xt1 2 "find the average rate of change of f from tox:...

Question

9 ? For x ~ #/ 1 Xt1 2 "find the average rate of change of f from tox:

9 ? For x ~ #/ 1 Xt1 2 " find the average rate of change of f from tox:



Answers

Find the average rate of change of $f(x)=9^{x}$ from $\frac{1}{2}$ to 1.

For average rate of change brought in our average rate of change formula. So this will be evaluated at tough of three minus F one divided by three minus one F of three is nine minus three. Squared, which is nine minus f of one is nine minus one squared, which is one all over three minus two, which is Excuse me, Q minus one, which is to all right nine minus 90 minus eight gives us a negative age over to which will give us a negative for.

Okay. To begin, we're gonna use the average rate of change formula, which says of X two minus f of X one over X two minus X one so we can go ahead and plug the two valleys into the function. So from here, we're gonna do square root of 16 minus two, squared of nine. And then this is only over X two minus at swung. Just 16 minutes night. So the squared of 16 is four, and the squared of mine is three. So 16 minus nine, which will give us seven and then on the top just simplifies toe one. So our average rate of change here is gonna be 17

Okay, So for this problem, we're gonna use the average rate of change formula which says so Average rate of change is equal to f of X two minus f of X one over X two minus X one. Okay, so from here, we can just plug in our x two and X one value. So in this case, what we have is squared of nine minus squared of four. So that's on top. And then we have X two minus x warm, which is just nine minus four. Scared of nine is three. Score to four is too, and the non minus four gives us five. Okay, so three minus two is just one. And then in the denominator, we have fought. So our average rate of change for this problem is 1/5.

We need to find the average rate of change of f of X is equal to three X squared minus two From 2- four. So I'm going to create a table. So when X is two we get three times two squared minus two. So that's three times four -2, which is 12 -2, which is 10. They were going to replace our next value, which is four, so we have three times four squared minus two, This becomes three times 16 -2, so that's 48 -2. So that's 46. So our average rate of change from here to here, we went up 36 from here to here, we went up to, So our average changes the change in Y over the change in X. So that's 36 over to. So our average rate of change is 18.


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