What is the minimum value of the expression \(2x^2+3y^2+8x-24y+62\) for real x and y?

mathtoo Aug 24, 2018

#1**+2 **

f (x, y) = 2x^2 + 3y^2 + 8x - 24y +62

Take partial derivatives in x and y and set these to 0

fx = 4x + 8 = 0 → x = -2

fy = 6y - 24 = 0 → y = 4

As WolframAlpha shows....(-2,4) * is* the min for this function.....and the min value = 6

https://www.wolframalpha.com/input/?i=minimize+%5B+2x%5E2%C2%A0+%2B+3y%5E2+%2B+8x+-+24y+%2B+62%5D

CPhill Aug 25, 2018