(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

For the function f(x, y, z) = z^4(x^2 − y^2), find the coordinates of

those points in the plane z = 1 at which the direction of the greatest rate of

change of f is parallel to the vector i − 2j + 3k.

2. Relevant equations

3. The attempt at a solution

i just want to verify that i am approaching this question correctly.

1.First, i substitute, z =1 into the equation.

2.so i get f(x,y,z) = x^2- y^2.

3. Then i find grad f(x,y,z). cos i need the direction of greatest rate of change. (i mean i find grad f of the equation x^2-y^2.)

4. To find the coodinates parallel to the vector i-2j+3k, i substitute

these values into my grad f equation.

MY WORKING:

As z= 1

f(x,y,z) = x^2 - y^2

grad f = 2xi - 2yj

Subsitute, x =1,y=-2 ->2xi-2yj

Therefore coordinates are: (2,4,0)

Could someone please tell me if this is correct.

Tanx

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Grad F question verification

**Physics Forums | Science Articles, Homework Help, Discussion**