Shown below is the fission yield curve for 233U (green curve), 235U (red curve),

Question

Shown below is the fission yield curve for 233U (green curve), 235U (red curve), 239Pu (blue curve) and a mixture of 65% U and 35% Pu (black curve). In your job as the Director of National Intelligence for the US you must report to the President whether or not the recent North Korean nuclear bomb test was based upon a 235U or 239Pu core. The US spy "sniffer" planes have returned from North Korea and the CIA radiochemists are looking at the samples the planes have collected. What do vou want them to pay special attention to so you can convince the President it was either a 235U or 239Pu core? 90 100 13 140 7% U-23 Tc u-239 6% 65%U 35%Pu 235 5% 4% 3% 1 2 2% 1% 80 90 120 15 160

Explanation / Answer

Remember that the derivative of a function is the slope of itstangent line.

Look at the points where the slope of the graphs become zero.Where one function has a slope of zero, its derivative must bezero.

Start by looking at the BLACK graph. It has horizontaltangents at about 2 and 4.9. Now look at the RED graph. It has zeros at both those values. Thatmeans the RED graph is the derivative ofthe BLACK graph.

Look at the RED graph again. It hashorizontal tangents at about 1 and at about 3.6. Now look atthe BLUE graph. It has zeros at boththose values. That means that the BLUEgraph is the derivative of the REDgraph.

Hence:

f (x) - BLACK

f '(x) - RED

f ''(x) - BLUE

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