Suppose that f(x, y) = 2? – ry + y² – 3z + 3y, with domain D constrained by the lines y = r, y = 0and z =3.The critical point of f(z, y) restricted to the boundary of D, but not at a corner point, is at (a, b), whereand b =a =The absolute minimum of f(z, y) isand the absolute maximum is

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Answered: Suppose that f(x, y) = x? – zy + y² –…

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.

Chapter9: Multivariable Calculus

Section9.3: Maxima And Minima

Problem 31E

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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.
Let f(x,y)=y22x2y+4x3+20x2. The only critical points are (2,4), (0,0), and (5,25). Which of the following correctly describes the behavior of f at these points? Source: Society of Actuaries. a. (2,4): local relative minimum (0,0): local relative minimum (5,25): local relative maximum b. (2,4): local relative minimum (0,0): local relative maximum (5,25): local relative maximum c. (2,4): neither a local relative minimum nor local relative maximum (0,0): local relative maximum (5,25): local relative minimum d. (2,4): local relative maximum (0,0): neither a local relative minimum nor local relative maximum (5,25): local relative minimum e. (2,4): neither a local relative minimum nor local relative maximum (0,0): local relative minimum (5,25): neither a local relative minimum nor local relative maximum

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Suppose that f(x, y) = x? – zy + y² – 3z + 3y, with domain D constrained by the lines y = z, y = 0 , and æ = 3. The critical point of f(x, y) restricted to the boundary of D, but not at a corner point, is at (a, b), where and b The absolute minimum of f(x, y) is and the absolute maximum is