Let J be a function of two variables such that its first and second partial derivatives are continuous throughot dis. centered at the point (5,1) and ,(5,1) = ,(5,1) = 0. Which of the following statements is true OA If f,„6, 1},„,(6, 1) – [,(5,1)]* <0 and f,(5,1) <0, then has a local maximum point. OB I S, 65, 1V„,(5,1) –[L(s,1)]* >0 and f,(5, 1) >0, then has a local mininmum point. OC Íf S„(5,1)f„,(5, 1) – [s,(5,1)]* >0 and f,(5,1) = 0, then f has a local maximum point. yx O D. No correct Answer If S„(6, 1Y,6, 1) [5,(5,1)]* >0 and f(5,1) >0, then has a local maximum point. OE.
Let J be a function of two variables such that its first and second partial derivatives are continuous throughot dis. centered at the point (5,1) and ,(5,1) = ,(5,1) = 0. Which of the following statements is true OA If f,„6, 1},„,(6, 1) – [,(5,1)]* <0 and f,(5,1) <0, then has a local maximum point. OB I S, 65, 1V„,(5,1) –[L(s,1)]* >0 and f,(5, 1) >0, then has a local mininmum point. OC Íf S„(5,1)f„,(5, 1) – [s,(5,1)]* >0 and f,(5,1) = 0, then f has a local maximum point. yx O D. No correct Answer If S„(6, 1Y,6, 1) [5,(5,1)]* >0 and f(5,1) >0, then has a local maximum point. OE.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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![Let J be a function of two variables such that its first and second partial derivatives are continuous throughot disk
centered at the point (5,1) and ,(5, 1) = ,(5,1) = 0. Which of the following statements is true
O A. If f„ (5, 1)f, (5,1) – f, (5,1) <0 and S, (5, 1) < 0, then has a local maximum point.
OB. If S, (5, 1)f,(5, 1) -[1,(5,1)] >0 and S„(5, 1) > 0, then / has a local mininmum point.
OC If f„ (5, 1)f,,(5, 1) - [S,(5,1)] >0 and S(5, 1) = 0, then S has a local maximum point.
O D. No correct Answer
If f„(5, 1)f,(5, 1) – ,5,1) >0 and S, (5, 1) > 0, then / has a local maximum point.
-
OE.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fad2ee818-08c0-4037-9a00-4c2dfb321687%2F89489d6d-e637-4789-9cb6-221585612568%2Fi84ta0h_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let J be a function of two variables such that its first and second partial derivatives are continuous throughot disk
centered at the point (5,1) and ,(5, 1) = ,(5,1) = 0. Which of the following statements is true
O A. If f„ (5, 1)f, (5,1) – f, (5,1) <0 and S, (5, 1) < 0, then has a local maximum point.
OB. If S, (5, 1)f,(5, 1) -[1,(5,1)] >0 and S„(5, 1) > 0, then / has a local mininmum point.
OC If f„ (5, 1)f,,(5, 1) - [S,(5,1)] >0 and S(5, 1) = 0, then S has a local maximum point.
O D. No correct Answer
If f„(5, 1)f,(5, 1) – ,5,1) >0 and S, (5, 1) > 0, then / has a local maximum point.
-
OE.
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