Let f (x, y) = y^2x − yx^2 + xy. (a) Show that the critical points (x, y) satisfy the equations y(y − 2x + 1) = 0, x(2y − x + 1) = 0 (b) Show that f has three critical points where x = 0 or y = 0 (or both) and one critical point where x and y are nonzero. (c) Use the Second Derivative Test to determine the nature of the critical points.

Let f (x, y) = y^2x − yx^2 + xy. (a) Show that the critical points (x, y) satisfy the equations y(y − 2x + 1) = 0, x(2y − x + 1) = 0 (b) Show that f has three critical points where x = 0 or y = 0 (or both) and one critical point where x and y are nonzero. (c) Use the Second Derivative Test to determine the nature of the critical points.

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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