Find the rate of change of f at P in the direction of the vector u. f(x,y,z)

Jaya Legge

Jaya Legge

Answered question

2021-09-13

Solve the rate of change of f at P in the direction of the vector u. f(x,y,z)=y2exyz, P(0,1,1), u=<313, 413, 1213>

Answer & Explanation

opsadnojD

opsadnojD

Skilled2021-09-14Added 95 answers

Recall that:
Rate of change of at P(a,b,c) in the direction of u is Duf
Where Duf(a,b,c)=f(a,b,c)u
Where u is unit vector
From part (b), we know that
f(0,1,1)=<1,2,0>
Given that u=<313,413,1213>, Note that it is already a unit vector
Duf(0,1,1)=f(0,1,1)u
Duf(0,1,1)=<1,2,0><313,413,1213>
Duf(0,1,1)=313+813+0=513
Result: Duf(0,1,1)=513

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