1. [-/2 Points] DETAILS WANEAC7 3.4.024. MY NOTES ASK YOUR...

1. [-/2 Points] DETAILS WANEAC7 3.4.024. MY NOTES ASK YOUR TEACHER Calculate the average rate of change of the given function f over the intervals [a, a + h] where h = 1, 0.1, 0.01, 0.001, and 0.0001. (Technology is recommended for the cases h = 0.01, 0.001, and 0.0001.) HINT [See Example 4.] f(x) = 4x^2 - 8x; a = 0 h = 1 h = 0.1 h = 0.01 h = 0.001 h = 0.0001 Submit Answer

Transcript

00:01 All right, for your question, you're asked to find the average rate of change for certain intervals.

00:05 Your intervals are built from a to a plus h, but you're given that a is going to remain a constant six, so your interval is really six to six plus h, and our h values are changing for each question.

00:21 So really what we want to do, is identify the intervals that we're going to be using.

00:26 The first interval would be from six to seven.

00:29 The second interval would be from 6 to 6 .1.

00:34 The third interval would be from 6 to 6 .01.

00:40 Fourth interval would be from 6 to 6 .001.

00:44 And the last interval would be from 6 to 6 .0001.

00:50 Now what we want to do is the first two, it says, i think you're trying to do by hand.

00:57 So we're going to need to know the value of f of 6, which would just be 5 over.

01:01 6.

01:02 We're going to need to know the value of f of 6 .1, which would be 5 over 6 .1.

01:13 And i'm going to go ahead, i'm sorry, we need f of 7 as well.

01:17 Sorry, i should have did that earlier.

01:18 F of 7 would be 5 over 7.

01:23 So for this first one, it's going to be your y value, your second y value, so the y value for the 7, which is 5 7s, minus your 1.

01:36 Your y value for the six, which is going to be the same for every question, 5 -6, over 7 minus 6.

01:47 So in this case, you could get a common denominator.

01:53 Looks like we can get a common denominator by multiplying by 6 here, by 7 here.

01:59 And i'm going to end up with 30 over 42 minus 35 over 42 over 42 over 42 over...

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