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a) Find the global maxima and minima for the function x² +2y? on the interior of the triangle with vertices (-1,2), (–1, –1), (2, –1).

a) Find the global maxima and minima for the function x² +2y? on the interior of the triangle with vertices (-1,2), (–1, –1), (2, –1).

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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a) Find the global maxima and minima for the function x² +2y? on the interior of the triangle with vertices (-1,2), (–1, –1), (2, –1). b) Compute the differential df for f(x, y) = sin(x)e™y?. c) Compute the differential dz and first order partials for a composite function z = x? + xy + y², x = r cos(0), y = rsin(0). d) Prove that f(t, x) = h(x – at) + h(x+ at) satisfies the wave equation fu – a? faa = 0 %3D for any differentiable twice function h(z).
Transcribed Image Text:a) Find the global maxima and minima for the function x² +2y? on the interior of the triangle with vertices (-1,2), (–1, –1), (2, –1). b) Compute the differential df for f(x, y) = sin(x)e™y?. c) Compute the differential dz and first order partials for a composite function z = x? + xy + y², x = r cos(0), y = rsin(0). d) Prove that f(t, x) = h(x – at) + h(x+ at) satisfies the wave equation fu – a? faa = 0 %3D for any differentiable twice function h(z).
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