Question

Under the condition 2x² + y² = 4 for REAL numbers, the maximum value of the equation 4x + y² is [6] and the minimum is [??]

Answer 1

So, I found the maximum value by 2x² + y² = 4 , y² = 4 - 2x² in the second equation...
But how can I find the minimum? ;-;

Answer 2

Ok so... I actually just found the minimum, using +sqrt(2) and -sqrt(2) as the boundary for
-2x²+4x+4

Answer 3

Since 2x²+y² =4 , the minimum and maximum value that x can assume is both when y=0, we have 2(x)² = 4 , x² = 2 , x = +sqrt(2) and -sqrt(2)