Use hessian matrix 2. Show that the following functions are convex by verifying the condition thatV² f(x) ≥ 0is satisfied for all a in the domain of f:(a) f(u₁, u₂) In(e" + e"),(b) f(u₁, U2, U3, U4) = ln(1-u₁-uz-us-u4) over the domain {u E R4|u₁ + ₂ + us+ us ≤ 1}.-

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Answered: 2. Show that the following functions…

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter14: Discrete Dynamical Systems

Section14.3: Determining Stability

Problem 4E

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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.
If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local extremum offon (a,c) ?
Determine if the statemment is true or false. If the statement is false, then correct it and make it true. If the function f increases on the interval -,x1 and decreases on the interval x1,, then fx1 is a local minimum value.

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2. Show that the following functions are convex by verifying the condition that ² f(x) 20 is satisfied for all a in the domain of f: (a) f(u₁, ₂) = n(e" +e"), (b) f(u₁, U2, U3, U4) = ln(1-₁-₂-3-4) over the domain {ue Rª|u₁ + 1₂ + 3 + ₁ ≤ 1}. -