- #1

- 16

- 0

I know

8x^7=(lamda)4x^3

8y^7=(lamda)4y^3

8z^7=(lamda)4z^3

x^4+y^4+z^4=4

Case1: x not equal to 0, y not equal to 0, and z not equal to 0

I get 3(4th root of 4/3 to the eigth)?

I'm I doing this right?

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- Thread starter jenc305
- Start date

- #1

- 16

- 0

I know

8x^7=(lamda)4x^3

8y^7=(lamda)4y^3

8z^7=(lamda)4z^3

x^4+y^4+z^4=4

Case1: x not equal to 0, y not equal to 0, and z not equal to 0

I get 3(4th root of 4/3 to the eigth)?

I'm I doing this right?

- #2

Science Advisor

Homework Helper

- 43,010

- 973

Since grad f always points in the direction of fastest increase of f, to get to a minimum, you should go in the exact opposite direction. Of course, if you are required to stay on the surface x

If you let g(x,y,z)= x

Yes, your formulas are correct!

If x is NOT 0, then, dividing the first equation by 8x

x

3x

However, it is not necessarily true that "either x,y,z are all 0 or they are all non-zero"! If x= 0, y= 0 but z is NOT 0, then z= 4

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