Is the second derivative of price negative if inflation's rate is decreasing?

[envanyatar]

I need help in the following question:
"The rate of increase of the rate of Inflation is decreasing" Write this sentence in terms of derivatives of average prices.

My answer: Let p=price
t= time
therefore, Rate of change of price = dp/dt = Inflation = I

therefore, rate of increase of the rate of Inflation = I'

therefore, I' = (d^2p)/(dt^2)

Since the rate of increase of the rate of Inflation is decreasing;

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

I just like to ask whether this is correct.
Thanks.

 

[whozum]

When a function f(x) is decreasing, $\frac{df}{dx}$ is always negative..