1. ## Maximum and Minimum

under the condition 2x²+y²=4 for real numbers x, y, the maximum value of 4x + y² is.....and the minimum one is .....

2. ## Re: Maximum and Minimum

show some work

3. ## Re: Maximum and Minimum

I thought...
y² = 4 - 2x²

4x + y² = 4x + 4 - 2x².....

maximum is (1,6), but the minimum?

I thought

4. ## Re: Maximum and Minimum

by derivate i get the maximum point but and the minimum?

5. ## Re: Maximum and Minimum

note that $2x^2+y^2 = 4$ is an ellipse with $-\sqrt{2} \le x \le \sqrt{2}$ and $-2 \le y \le 2$

the value of $4x+y^2$ will be a minimum when $x = -\sqrt{2}$ and $y=0$

thanks!!!