Is the rate of change of Inflation negative?

[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.

My answer was:
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.
Please help.

 

[quantumdude]

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.

My answer was:
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)

So far, so good.

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

I just wanted to check whether my answer is correct.

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

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

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

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'?

 

[envanyatar]

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

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

 

[HallsofIvy]

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?

 

[quantumdude]

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

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?