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Find f(x,y) = ²x³+yª−xy+1 for −2≤x≤2; 2≤y≤2 a) fx fyfxx fyy,fxy. b) the critical points of f(x,y). Hence, classify the critical points as local minimum/maximum or saddle point. c) the local maximum/minimum value of f(x,y).

Find f(x,y) = ²x³+yª−xy+1 for −2≤x≤2; 2≤y≤2 a) fx fyfxx fyy,fxy. b) the critical points of f(x,y). Hence, classify the critical points as local minimum/maximum or saddle point. c) the local maximum/minimum value of f(x,y).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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You are designing a structure with smart sensors. The sensors are to be placed at critical points of the structure. Suppose that a function describing the structure as shown above is given by Find f(x, y) = = ²x³ + y² = x - xy + 1 for 2 ≤ x ≤2; 2≤ y ≤ 2 a) fx¹fy, fxx fyy,fxy. b) the critical points of f(x,y). Hence, classify the critical points as local minimum/maximum or saddle point. c) the local maximum/minimum value of f(x,y).
Transcribed Image Text:You are designing a structure with smart sensors. The sensors are to be placed at critical points of the structure. Suppose that a function describing the structure as shown above is given by Find f(x, y) = = ²x³ + y² = x - xy + 1 for 2 ≤ x ≤2; 2≤ y ≤ 2 a) fx¹fy, fxx fyy,fxy. b) the critical points of f(x,y). Hence, classify the critical points as local minimum/maximum or saddle point. c) the local maximum/minimum value of f(x,y).
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