- #1

- 45

- 8

## Homework Statement

Find the local extreme values of ƒ(x, y) = x2y on the line x + y = 3

## Homework Equations

∇ƒ = λ∇g

## The Attempt at a Solution

2yx

**i**+x^2

**j**= λ

**i**+ λ

**j**

[2yx=λ] [x^2=λ] [x+y=3]

[2yx=x^2] & [(2y)+y=3]

[2y=x] & [y=1]

x=2

This is as far as I got, and gives f(2,1)=4 as the extreme value. The solution I have (chegg.com) lists another possible solution.

On the left column, they give another solution to the equation 2y=x:

They say:

2y=x

x=0

and proceed to use the "x+y=3" equation to give an alternative extrema which is f(0,3)

Can anyone explain how they made the jump from 2y=x to x=0?

Why isn't y=0 another solution? (If x equals and 2y equals x, then y must equal zero)

Thanks in advance, screenshot from solution below

-Rudy