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Q. 29

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 directional derivative of the given function at the specified point P in the direction of the given vector. Note: The given vectors may not be unit vectors.



See the step by step solution

Step by Step Solution

Step 1. Given Information

The directional derivative of a function f(x,y,z) at a point P=x0,y0,z0 in the direction of a unit vector u=a,b,c is given by Dufx0,y0,z0=limh0fx0+ah,y0+bh,z0+chfx0,y0,z0h Here f(x,y,z)=xy2z3, and P=(0,0,0).

Step 2. Solution

Also the vector is v=1,2,1 The unit vector " u " in the direction of " v" is given by u=1vv=112+(2)2+(1)21,2,1=161,2,1 Hence the directional derivative is: Duf(0,0,0)=limh0fh6,2h6,h6f(0,0,0)h=limh0h62h62h630h=limh04h563=0Hence Duf(0,0,0)=0

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