Second Derivative Test. Consider the functionf(x,y) = 4xy + 2ln(x) + 8y(a) The critical point of f(x,y) is(1,-1)There is no critical point(0,0)O (-1/2,2)O (1,e)O (-2,1/4)O (e,1)O (-1,1)(b) Use the second derivative test for functions of two variables to determine that in part (a):the critical point is a local minimumthe second derivative test is inconclusivethe critical point is not in the domainthe critical point is a local maximumthe critical point is a saddle point

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Answered: Second Derivative Test. Consider the…

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Calculus

Second Derivative Test. Consider the function f(x,y) = 4xy + 2ln(x) + 8y

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 15E

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Question

Second Derivative Test. Consider the function
f(x,y) = 4xy + 2ln(x) + 8y
(a) The critical point of f(x,y) is
(1,-1)
There is no critical point
(0,0)
O (-1/2,2)
O (1,e)
O (-2,1/4)
O (e,1)
O (-1,1)
(b) Use the second derivative test for functions of two variables to determine that in part (a):
the critical point is a local minimum
the second derivative test is inconclusive
the critical point is not in the domain
the critical point is a local maximum
the critical point is a saddle point

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