Need Help with calculus qustion plz? (1 Viewer)

[CJ251]

Hi everyone. Hope everyones doin gud and studyin hard. I jus got a question on calculus.

"Although the amount of pollution is increasing, The Government's policies to reduce pollution seems to be taking effect."

Given that P is the amount of pollution, what does the above statement imply about dP/dt and d squared P/dt squared.

If you could explian why it would be greatly appreciated. Thanks heaps.

 

[pLuvia]

dP/dt is the rate in which pollution is increasing, hence dP/dt>0, hence increasing. But the gov't is reducing it, so although it is increasing, the it is a maximum for the d²P/dt²

 

[CJ251]

dP/dt is the rate in which pollution is increasing, hence dP/dt>0, hence increasing. But the gov't is reducing it, so although it is increasing, the it is a maximum for the d²P/dt²

Thanks pluvia
but why is d2p/dt2 a mximum if the gov't is trying to reduce it. Im a bit slow

 

[SoulSearcher]

d²P/dt² is a maximum because if there was a minimum, the pollution would be increasing at an increasing rate, rather than increasing at a decreasing rate, which the government is doing.

 

[ThuanSUX]

Simply put:

The pollution is increasing, but at a decreasing rate.

dP/dT > 0 and d2P/dT2 < 0
Thus, it's a maximum.

 

[Mumma]

Look at the attatched graph.
P = f(x)
Even though P is increasing, as said above, its increasing at a decreasing rate.
In other words, the graph looks like its concaving downwards.

So, P is increasing
Therefore dP/dt > 0
But, the rate of increase (ie. dP/dt) is decreasing
Therefore, d²P/dt² < 0