Consider a function defined on R² by f(x, y) = y(x + 1)(2 − x − y). (a) Find all four critical points of the function f(x, y). (b) For the critical points not lying in the x-axis, calculate the Hessian matrix for each of them and determine whether the critical point is local maximum/minimum or saddle.

Consider a function defined on R² by f(x, y) = y(x + 1)(2 − x − y). (a) Find all four critical points of the function f(x, y). (b) For the critical points not lying in the x-axis, calculate the Hessian matrix for each of them and determine whether the critical point is local maximum/minimum or saddle.

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 13E: Repeat the instruction of Exercise 11 for the function. f(x)=x3+x For part d, use i. a1=0.1 ii...

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