1-Which of the following is the most complete characterization of a critical poi
ID: 2833510 • Letter: 1
Question
1-Which of the following is the most complete characterization of a critical point for a multivariable function?
options:
(a,b) is a critical point if f_x(a,b)=0 and f_y(a,b)=0 (where f_x is the partial derivative of f with respect to x).
(a,b) is a critical point if f_x(a,b)=0 and f_y(a,b)=0 (where f_x is the partial derivative of f with respect to x) OR if at least one of f_x(a,b) or f_y(a,b) do not exist.
(a,b) is a critical point if f(a,b)=0 and f(a,b)=0
(a,b) is a critical point if f_xx(a,b)=f_yy(a,b)
2-In the second derivative test for multivariable functions, if the discriminant at a point (a,b) is greater than zero, D(a,b)>0, then:
Question 2 options:
(a,b) is either a max or a min
(a,b) is a saddle point
(a,b)>0
The second derivative test is inconclusive
3-For two variable functions, all max/min points are critical points, but a critical point may or may not be a max or a min.
True
False
4-When finding the max/min points on a closed, bounded region, one must find the max/min points on the interior of the region as well as the max/min points along the boundaries and vertices of the region.
True
False
5- A critical point that is not a maximum or a minimum is typically called
Question 5 options:
a saddle point
an attraction point
a Hessian point
Such a point cannot exist
(a,b) is a critical point if f_x(a,b)=0 and f_y(a,b)=0 (where f_x is the partial derivative of f with respect to x).
(a,b) is a critical point if f_x(a,b)=0 and f_y(a,b)=0 (where f_x is the partial derivative of f with respect to x) OR if at least one of f_x(a,b) or f_y(a,b) do not exist.
(a,b) is a critical point if f(a,b)=0 and f(a,b)=0
(a,b) is a critical point if f_xx(a,b)=f_yy(a,b)
2-In the second derivative test for multivariable functions, if the discriminant at a point (a,b) is greater than zero, D(a,b)>0, then:
Question 2 options:
(a,b) is either a max or a min
(a,b) is a saddle point
(a,b)>0
The second derivative test is inconclusive
3-For two variable functions, all max/min points are critical points, but a critical point may or may not be a max or a min.
True
False
4-When finding the max/min points on a closed, bounded region, one must find the max/min points on the interior of the region as well as the max/min points along the boundaries and vertices of the region.
True
False
5- A critical point that is not a maximum or a minimum is typically called
Question 5 options:
a saddle point
an attraction point
a Hessian point
Such a point cannot exist
Explanation / Answer
1) (a,b) is a critical point if f_x(a,b)=0 and f_y(a,b)=0 (where f_x is the partial derivative of f with respect to x).
2) (a,b) is either a max or a min
3) true
4) true
5) saddlrpoint
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