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(d) Find the directional derivative of f at (-2,1), in the direction of (-3,5).

(d) Find the directional derivative of f at (-2,1), in the direction of (-3,5).

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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Given: f(x,y)=9-x^2- y^2
(d) Find the directional derivative of \( f \) at \((-2, 1)\), in the direction of \(\langle -3, 5 \rangle\).
Transcribed Image Text:(d) Find the directional derivative of \( f \) at \((-2, 1)\), in the direction of \(\langle -3, 5 \rangle\).
Expert Solution
Step 1

Given f(x,y)=9-x2-y2

fx= -2x

fy=-2y

∇f(x,y)=<fx,fy>=<-2x,-2y>

∇f(-2,1)=<-2(-2),-2(1)>=<4,-2>

unit vector u= <-3,5>(-3)2+52=<-3,5>9+25

                      =<-3,5>34

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