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Q. 31

Found in: Page 989


Book edition 1st
Author(s) Peter Kohn, Laura Taalman
Pages 1155 pages
ISBN 9781429241861

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Short Answer

Find the gradient of the given function, and find the direction in which the function increases most rapidly at the specified point P.



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Step by Step Solution

Step 1. Given Information

The gradient of a function f(x,y) is the vector function defined by f(x,y)=fxi+fyj Here f(x,y)=yx.

Step 2.Solution

Gradient is given by,f(x,y)=xyxi+yyxj=yx2i+1xjTherefore, f(x,y)=yx2,1x As the gradient of a function f at a point p, points in the direction in which f increases most rapidly. At p=(4,3),f(4,3)=316i+14jHence the direction at which f increases most rapidly at p=(4,3) is f(4,3)=316,14

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