Consider the two-variable function $f(x, y) = x^ 2 + 2y^2$
(a) Find the maxima and minima of $f(x, y)$ on the unit circle $x^2 +y^2 = 1$
I have used lagrange multipies to get landa= to $1$ or $2$. Given the points$(1,0),(-1,0),(0,1),(0,-1)$. so the min would be at $(0,0)$ and the max at $(0,-1)$ and $(0,1)$
Am i right in thinking this?
Secondandly how can i sketch a contour plot of this question to show graphically mypoints of maximum and minimum. I am aware its an ellipse contour.