00:01
In this question, we want to find the average rate of change of the function over the given interval or intervals.
00:06
And here i have the function g of t, which is equal to 2 plus the cosine of t.
00:13
Now, in part a, we're on the closed interval from 0 to pi.
00:18
So how do i find an average rate of change? an average rate of change is a slope of a secant line.
00:25
So in general, it's f of b minus f of a being divided by b minus a.
00:30
So in this case, we're going to have g evaluated at pi minus g evaluated at 0 over pi minus 0.
00:43
So now, what is g of pi? well, g of pi is 2 plus the cosine of pi.
00:50
The cosine of pi is negative 1.
00:55
So 2 plus negative 1 gives you 1.
00:59
You also need g of 0.
01:01
So g of 0 would be 2 plus the cosine of 0.
01:05
The cosine of 0 is 1.
01:08
So 2 plus 1 gives you 3.
01:12
So we're getting g of pi 1 minus g of 0 3 over pi minus 0, which is pi...