Rate of outflow in gallons per hour

[fdragon]

The rate at which water flows out of a pipe, in gallons per hour, is given by a differentiable function R of time t. The table shows the rate as measured every 3 hours for a 24 hour period.

--------------
0 9.6
3 10.4
6 10.8
9 11.2
12 11.4
15 11.3
18 10.7
21 10.2
24 9.6


.... Is there some time t, 0 <t< 24, such that R'(t)= 0? Justify your answer.

 

[galactus]

You can use Excel or a good calculator to perform a regression analysis.

From your data you can see there is such a point because the rate goes up and then starts to go down. This would imply there is a maximum output point, whereby f'(x) will be 0.

Do you have a nice calculator which will do it?. Excel works great for this sort of thing.

 

[skeeter]

hint ... Mean Value Theorem used between the endpoints of the data.

 

[galactus]

I see skeeter. Deleted due to redundancy.

 

[skeeter]

This is a question from a recent AP exam.

Note that the question is asking about the existence of some t in the given interval where R'(t) = 0 rather than the actual value of t where R'(t) = 0.

Note also that the question tells you that R is differentiable (and hence, continuous).

The MVT states that there must exist at least one time where
R'(t) = [R(24) - R(0)]/(24 - 0) = 0

 

[fdragon]

OMG I love you guys. lol