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Determine the stationary points of the function f(x, y) = 3xy + y - 4x – 4y + 6. Find its local minima, local maxima and saddle points. PIO.24

Determine the stationary points of the function f(x, y) = 3xy + y - 4x – 4y + 6. Find its local minima, local maxima and saddle points. PIO.24

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 vector field is given by F = -yê, + zê, + x'ê̟. Determine its line integral over a circular path of radius R in the XY-plane, with its center at the origin. Determine if the Stokes' theorem holds good for this circular path, by considering the following surfaces: PIO.20 (1) the plane of the circle, and (ii) surface of a cylinder of height h erected on the circle. o co Determine the curl of the following vectors fields: (a) p cos pê, - p sin pê, (b) -ě,. For the steady irrotational flow of incompressible, non-viscous liquids, if the flow occurs under gravity, find the value of pressure at an arbitrary height, z. PIO.21 PIO.22 PIO.23 The density field of a plane, steady state fluid flow given by P(x1, x2)=kx,x2 where k is constant. Determine the form of the velocity field if the fluid is incompressible. Determine the stationary points of the function f(x, y) = 3x'y +y – 4x – 4y + 6. Find its local minima, local maxima and saddle points. PIO.24 %3!
Transcribed Image Text:A vector field is given by F = -yê, + zê, + x'ê̟. Determine its line integral over a circular path of radius R in the XY-plane, with its center at the origin. Determine if the Stokes' theorem holds good for this circular path, by considering the following surfaces: PIO.20 (1) the plane of the circle, and (ii) surface of a cylinder of height h erected on the circle. o co Determine the curl of the following vectors fields: (a) p cos pê, - p sin pê, (b) -ě,. For the steady irrotational flow of incompressible, non-viscous liquids, if the flow occurs under gravity, find the value of pressure at an arbitrary height, z. PIO.21 PIO.22 PIO.23 The density field of a plane, steady state fluid flow given by P(x1, x2)=kx,x2 where k is constant. Determine the form of the velocity field if the fluid is incompressible. Determine the stationary points of the function f(x, y) = 3x'y +y – 4x – 4y + 6. Find its local minima, local maxima and saddle points. PIO.24 %3!
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