Rate of fuel consumtion

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kaebun

Junior Member
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Sep 11, 2005
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135
This problem is going to be difficult to type out but I'll do my best...

Table: t (minutes).........R(t) (gallons per minute)
0.......................20
30.....................30
40.....................40
50.....................55
70.................... 65
90.....................70

There was also a graph, but I can't type that :), but I don't think you need it (at least I hope you don't).

The question The rate of fuel consumtion, in gallons per minute, recorded during an airplane flight is given by a twice differentiable function and strictly increasing function R of time t.

a)use the data from the table to find an approximation for R'(45)

what I did was take the find the slope between 40 and 50,

55-40/50-40= 1.5

which I guess makes sense what confusses me is the next question

b) The rate of fuel consumtion is increasing fastest at t=45. What is the value of R"(45)?

to do this I took the derivitive of 1.5, which is zero.
But the problem says that it is "increasing fastest" , which doesn't fit this answer.

Thanks for your help,
Kathy
 
There is an inconsistency in your post. You write (50,50) in the table but use (50,55) in your calculations. But in any case, the second derivative tells us how the first derivative is changing. Remember, maximal and minimal values occur if the function (in this case the first derivative) has a critical point.
 
Sorry about that, the point is (50,55), I've fixed that now.
I understand what your saying, but I'm not sure how to apply it to the problem. All its done as confirmed my belief that my answer to B is wrong. I have no idea how to find the correct answer with no equation.
 
If \(\displaystyle f''(x) = 0\) then \(\displaystyle f'(x)\) has a critical point.
 
I think I just got it... the answer to B would be zero because the slope of the R'(t) would be switching from positive to negitive. Is that right?
 
how funny is that I got it just before you replied...
One more question it asks what the intregal of the function represents, it would be the amount of fuel right?
 
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