### Video Transcript

The average rate of change of
π as π₯ varies from two to 2.6 is negative 1.67. If π of two is equal to
negative 13, what is π of 2.6?

Remember, the average rate of
change of a function π as π₯ varies from π to π plus β is given by π of π
plus β minus π of π over β. Now, in this question, we donβt
actually know what π of π₯ is. But we do see that π₯ varies
from two to 2.6. So, we let π be equal to
two. And then, β is the amount π₯
varies by. Itβs 2.6 minus two, which is
0.6. We want to find the average
rate of change function, so thatβs π΄ of β, which is π΄ of 0.6. And so, according to our
formula, thatβs π of two plus 0.6 minus π of two over 0.6. This simplifies to π of 2.6
minus π of two over 0.6.

Weβre told, however, that this
is equal to negative 1.67, and also that π of two is equal to negative 13. So, we find that negative 1.67
must be equal to π of 2.6 minus negative 13 over 0.6. To find π of 2.6 as this
question is asking us, we need to solve this equation for π of 2.6. Weβll begin by multiplying
through by 0.6. And that gives us negative
1.002 on the left. And then on the right, weβre
left with π of 2.6 minus negative 13, which is, of course, π of 2.6 plus
13. Next, we subtract 13 from both
sides, and we find that π of 2.6 is negative 14.002. Correct to the nearest whole
number, π of 2.6 is negative 14.