Polkulus 2

F(Polk)=Polk^2+4(Polk)+4=Expansionism on the interval [-4, 10] when -4=East and 10=West

The Mean Value Theorem does apply because Expansionism is continuous from East to West. But what is the Average Rate of Change in Expansionism and at what point in the West is it reached if that point is Dark Horse?

F(East)=4, F(West)=144

m(Secant Slope of Democracy)=(144-4)/(10-(-4))= 10

At what Polk point will F'(Polk)=10?

d/dx (Expansionism) —> dy/dx=2(Polk)+4

Therefore when 2(Polk)+4=10…

2(Polk)=6

Polk=3

Dark Horse=3

Expansionism is at its Average Rate of Change at F(Dark Horse)=25.