00:01
Hi there, so for this problem, we need to estimate the instantaneous rate of change of the function that we are given, and that function f of x is equal to minus x squared plus two times x, and this at the value of x equals to minus two.
00:18
So this, using the average rate of change over successively smaller intervals.
00:25
Okay.
00:26
Now, with that said, the first interval that we're going to choose is interable between, the initial and well the initial value of minus two to a final value of minus 2 .01.
00:42
So the average rate of change for this function is this function evaluated at the last point which is minus 2 .01 and then this minus this function evaluated at the initial point minus 2 and this is divided by the difference between this two.
01:00
So the difference is minus 2.
01:03
0 .01 plus 2.
01:05
So that will give us minus 0 .01 in here.
01:11
Now we just need to do the evaluation for this.
01:14
So that will do.
01:15
The function evaluated at these two values.
01:17
So that will be minus minus 2 .01 and back to the square.
01:23
And then this minus 2 times 2 .01.
01:27
And then this minus 2 times 2 .01.
01:31
And then this minus that will be plus in here, and then this will be minus 2, and that to the square, and then this, that will be 2, 2 times 2, okay? and then this, they got it by 0 .01.
01:57
So using our calculator, we obtain a value of, so let's see...