Consider all points in the plane that solve the equation \(x^2+2y^2=16\). Find the maximum value of the product \(xy\) on this graph.

(In case the LaTeX doesn't render)--Consider all points in the plane that solve the equation x^2 + 2y^2 = 16. Find the maximum value of the product xy on this graph.

Guest Jan 26, 2020

#1

#5**+1 **

Consider all points in the plane that solve the equation x^2 + 2y^2 = 16. Find the maximum value of the product xy on this graph.

Doing it graphically I get approx 5.66

Melody Jan 27, 2020

#7

#8**+1 **

I gave you an answer, I do not see your thanks.

It is easy enough to get an exact answer using calculus.

\(x=\sqrt{16-2y^2}\\ let \;\;M=xy\\ M=y*\sqrt{16-2y^2}\\ Find \quad dM/dy\\ \text{put it equal to 0 to find the stationary points.}\\ \text{Solve for y}\\ \text{Substitute to find M}\\ \text{if you are feeling keen you should prove that this is a maximum.}\\ \text {This will give you the exact value that i have already approximated via the graph.}\\ \)

Melody
Jan 27, 2020