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Part B needed please Kindly solve in 20 minutes and get the thumbs up please show me neat and clean work for it by hand solution needed Kindly solve ASAP in the order to get positive feedback with hundred percent efficiency

Part B needed please Kindly solve in 20 minutes and get the thumbs up please show me neat and clean work for it by hand solution needed Kindly solve ASAP in the order to get positive feedback with hundred percent efficiency

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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Part B needed please Kindly solve in 20 minutes and get the thumbs up please show me neat and clean work for it by hand solution needed Kindly solve ASAP in the order to get positive feedback with hundred percent efficiency
(a) Consider the function f: R2 → R where f(x, y) = cos(x²y).- (i) Find all the first and second order partial derivatives. (You may assume that fay = fyx.) (ii) Calculate the differential df of the function f(x, y) at the points (a,0), a € R and (0, b), b = R. (iii) Compute the directional derivative of f at (1, π/2) in the direction of v=i+j. (b) Consider the function g(x, y) = x² + 2xy + 2xy². (i) Show that (0, 0) is a critical point and find any other critical point(s) of g. (ii) Classify the critical point (0, 0) of g(x, y) as a local maximum, a local minimum or a saddle. (iii) Is g(0,0) a global maximum of g(x, y), a global minimum of g(x, y) or neither? Justify your answer.
Transcribed Image Text:(a) Consider the function f: R2 → R where f(x, y) = cos(x²y).- (i) Find all the first and second order partial derivatives. (You may assume that fay = fyx.) (ii) Calculate the differential df of the function f(x, y) at the points (a,0), a € R and (0, b), b = R. (iii) Compute the directional derivative of f at (1, π/2) in the direction of v=i+j. (b) Consider the function g(x, y) = x² + 2xy + 2xy². (i) Show that (0, 0) is a critical point and find any other critical point(s) of g. (ii) Classify the critical point (0, 0) of g(x, y) as a local maximum, a local minimum or a saddle. (iii) Is g(0,0) a global maximum of g(x, y), a global minimum of g(x, y) or neither? Justify your answer.
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