Evaluate the maximum rate of change of f(x,y) = ln(x^2+y^2)

chillywilly12a

chillywilly12a

Answered question

2021-08-17

Evaluate the maximum rate of change of f(x,y)=ln(x2+y2) at the point (3,2) and the direction in which it occurs.
What is maximum rate of change and direction(unit vector) in which it occurs?

Answer & Explanation

Luvottoq

Luvottoq

Skilled2021-08-18Added 95 answers

f(x,y)=ln(x2+y2) at (3,2)
For max rate of change, take gradient
f=fxi+fyj=
=<1x2+y22x,1x2+y22y>=
=2x2+y2<x,y>
at (3,2) =232+22<3,2>=
=213<3,2>
This is the direction for max rate
Direction(unit vector) in which it occurs: <2,3>13
Maximum rate of change: 21332+22=213

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