# Differential eq problem

1. Oct 18, 2005

### envanyatar

Differential eq problem (urgent)

I have the following question which I was to answer:
"The rate of increase of the rate of inflation is decreasing". Write this sentence in terms of derivatives of average prices.

Let p=price
t=time
Therefore rate of change of price = dp/dt (Inflation) = I

Therefore rate of change of Inflation = I'

Therefore I'= (d^2p)/(dt^2)

Since the rate of change of Inflation is decreasing;

I' = - (d^2p)/(dt^2)

I just wanted to check whether my answer is correct.

2. Oct 19, 2005

### Tom Mattson

Staff Emeritus
So far, so good.

Your answer is not correct, and if you look at two of your lines side by side it should be clear why:

If I' simultaneously equals both (d^2p)/(dt^2) and - (d^2p)/(dt^2), then I' can only be zero, which is obviously not true.

Your first definition of I' is correct. So, if I is decreasing then what mathematical statement would you say about I'?

3. Oct 20, 2005

### envanyatar

So if dI/dt is decreasing, is the I' negative? (i.e. -I')?

4. Oct 20, 2005

### HallsofIvy

Staff Emeritus
Actually, if I read this correctly, there is another problem that has not been addressed:
"The rate of increase of the rate of inflation is decreasing"

Yes, the "rate of inflation" is dp/dt. Yes, the "rate of increase of the rate of inflation" is d2p/dt2. Now you want say that that is decreasing. What must be true of its derivative (i.e. d3p/dt3?

5. Oct 20, 2005

### Tom Mattson

Staff Emeritus
No, you're just making the same mistake all over again. If I'=-I', then I' can only be zero.

Think about it, if you want to say that x is negative then you don't say that x is -x, you say that x is less than zero.

So how do you write that down in mathematical symbols?