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- Repeat the instruction of Exercise 11 for the function. f(x)=x3+x For part d, use i. a1=0.1 ii a1=0.1 11. Consider the function f(x)=4x2(1x) a. Find any equilibrium points where f(x)=x. b. Determine the derivative at each of the equilibrium points found in part a. c. What does the theorem on the Stability of Equilibrium points tell us about each of the equilibrium points found in part a? d. Find the next four iterations of the function for the following starting values. i. a1=0.4. ii. a2=0.7 e. Describe the behavior of successive iteration found in part d. f. Discuss how the behavior found in part d relates to the results from part c.7. Determine whether (u,v) =3u, v, – 2u, v, is a valid inner-product function or not for R %3Db) Let aggregate national income be given by Y; = Ct + It + Gt Where C, I and G are consumption, investment and government expenditure. Assume that consumption is given by Ct = mY; Investment is given by Iį = i + a(Yt-1 – Yt-2) And government expenditure declines over time according to G; = Go(1 – 8)*, 0 < 8 < 1 Where d is the exogenous rate of decline of government expenditure (i) Derive the linear second order difference equation. (ii) Solve the difference equation.
