Here is the question:

Find the extrema of \(\displaystyle f(x, y) = x + y^2\), with constraint : \(\displaystyle 2x^2 + y^2 = 1\)

My attempts at solution:

I tried to solve it using Lagrange multiplier and I got:

\(\displaystyle 1 = 4x \lambda \) ............................. I

\(\displaystyle 2y = 2y \lambda\) ............................. II

\(\displaystyle 2x^2 + y^2 = 1 \) ............................. III

Now here is where I am stuck. How can I use the first two equations to get the value of either x or y?

Find the extrema of \(\displaystyle f(x, y) = x + y^2\), with constraint : \(\displaystyle 2x^2 + y^2 = 1\)

My attempts at solution:

I tried to solve it using Lagrange multiplier and I got:

\(\displaystyle 1 = 4x \lambda \) ............................. I

\(\displaystyle 2y = 2y \lambda\) ............................. II

\(\displaystyle 2x^2 + y^2 = 1 \) ............................. III

Now here is where I am stuck. How can I use the first two equations to get the value of either x or y?

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