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Find the critical points of the following function. Use the Second Derivative Test to determine​ (if possible) whether each critical point corresponds to a local​ maximum, local​ minimum, or saddle point. If the Second Derivative Test is​ inconclusive, determine the behavior of the function at the critical points. f(x,y) = sqrt(x2+y2+2x2+10)

Find the critical points of the following function. Use the Second Derivative Test to determine​ (if possible) whether each critical point corresponds to a local​ maximum, local​ minimum, or saddle point. If the Second Derivative Test is​ inconclusive, determine the behavior of the function at the critical points. f(x,y) = sqrt(x2+y2+2x2+10)

Calculus For The Life Sciences
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.
Chapter6: Applications Of The Derivative
Section6.CR: Chapter 6 Review
Problem 1CR
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Find the critical points of the following function. Use the Second Derivative Test to determine​ (if possible) whether each critical point corresponds to a local​ maximum, local​ minimum, or saddle point. If the Second Derivative Test is​ inconclusive, determine the behavior of the function at the critical points. f(x,y) = sqrt(x2+y2+2x2+10)

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Find the critical points of the following function. Use the Second Derivative Test to determine (if possible) whether each critical point corresponds to a local maximum, local minimum, or saddle point. If the Second Derivative Test is inconclusive, determine the behavior of the function at the critical points. f(x,y)=√√x² + y² + 2x + 10 A. The test shows that there is/are local minima at (-1,0). (Type an ordered pair. Use a comma to separate answers as needed.) B. The test does not reveal any local minima and there are no critical points for which the test is inconclusive, so there are no local minima. C. The test does not reveal any local minima, but there is at least one critical point for which the test is inconclusive. Use the Second Derivative Test to find the saddle points. Select the correct choice below and fill in any answer boxes within your choice. A. There is/are saddle point(s) at (Type an ordered pair. Use a comma to separate answers as needed.) B. The test does not reveal any saddle points and there are no critical points for which the test is inconclusive, so there are no saddle points. C. The test does not reveal any saddle points, but there is at least one critical point for which the test is inconclusive. Determine the behavior of the function at any of the critical points for which the Second Derivative Test is inconclusive. Select the correct choice below and, if necessary, fill in the answer box(es) within your choice. A. Among these points, there are local maximum/maxima at (Type an ordered pair. Use a comma to separate answers as needed.) B. , F. G. " local minimum/minima at and no saddle points. Among these points, there are local maximum/maxima at and no local minima or saddle points. (Type an ordered pair. Use a comma to separate answers as needed.) D. Among these points, there are local maximum/maxima at (Type an ordered pair. Use a comma to separate answers as needed.) Among these points, there are local minimum/minima at and no local maxima or saddle points. (Type an ordered pair. Use a comma to separate answers as needed.) " E. Among these points, there are local maximum/maxima at saddle point(s) at (Type an ordered pair. Use a comma to separate answers as needed.) local minimum/minima at and saddle point(s) at " Among these points, there are local minimum/minima at saddle point(s) at (Type an ordered pair. Use a comma to separate answers as needed.) 3 H. The Second Derivative Test is conclusive for each critical point. " Among these points, there are saddle point(s) at and no local maxima or minima. (Type an ordered pair. Use a comma to separate answers as needed.) 3 " and no local minima. and no local maxima.
Transcribed Image Text:Find the critical points of the following function. Use the Second Derivative Test to determine (if possible) whether each critical point corresponds to a local maximum, local minimum, or saddle point. If the Second Derivative Test is inconclusive, determine the behavior of the function at the critical points. f(x,y)=√√x² + y² + 2x + 10 A. The test shows that there is/are local minima at (-1,0). (Type an ordered pair. Use a comma to separate answers as needed.) B. The test does not reveal any local minima and there are no critical points for which the test is inconclusive, so there are no local minima. C. The test does not reveal any local minima, but there is at least one critical point for which the test is inconclusive. Use the Second Derivative Test to find the saddle points. Select the correct choice below and fill in any answer boxes within your choice. A. There is/are saddle point(s) at (Type an ordered pair. Use a comma to separate answers as needed.) B. The test does not reveal any saddle points and there are no critical points for which the test is inconclusive, so there are no saddle points. C. The test does not reveal any saddle points, but there is at least one critical point for which the test is inconclusive. Determine the behavior of the function at any of the critical points for which the Second Derivative Test is inconclusive. Select the correct choice below and, if necessary, fill in the answer box(es) within your choice. A. Among these points, there are local maximum/maxima at (Type an ordered pair. Use a comma to separate answers as needed.) B. , F. G. " local minimum/minima at and no saddle points. Among these points, there are local maximum/maxima at and no local minima or saddle points. (Type an ordered pair. Use a comma to separate answers as needed.) D. Among these points, there are local maximum/maxima at (Type an ordered pair. Use a comma to separate answers as needed.) Among these points, there are local minimum/minima at and no local maxima or saddle points. (Type an ordered pair. Use a comma to separate answers as needed.) " E. Among these points, there are local maximum/maxima at saddle point(s) at (Type an ordered pair. Use a comma to separate answers as needed.) local minimum/minima at and saddle point(s) at " Among these points, there are local minimum/minima at saddle point(s) at (Type an ordered pair. Use a comma to separate answers as needed.) 3 H. The Second Derivative Test is conclusive for each critical point. " Among these points, there are saddle point(s) at and no local maxima or minima. (Type an ordered pair. Use a comma to separate answers as needed.) 3 " and no local minima. and no local maxima.
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