(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 tha (ii) Calculate the differential df of the function f(x, y) at the points (a, 0), c (0, b), b € R. (iii) Compute the directional derivative of f at (1, π/2) in the direction of (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 minin saddle. (iii) Is g(0,0) a global maximum of g(x, y), a global minimum of g(x, y) or neit your answer.

(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 tha (ii) Calculate the differential df of the function f(x, y) at the points (a, 0), c (0, b), b € R. (iii) Compute the directional derivative of f at (1, π/2) in the direction of (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 minin saddle. (iii) Is g(0,0) a global maximum of g(x, y), a global minimum of g(x, y) or neit your answer.

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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