IIT JEE , AIEEE Forum - Mathematics , Differential Calculus - find min value of x^2 + 2xy + 3y^2 -6x

little_genius

let us first fix the value of y and then vary x to find the minimum value of func. for that fixed value of y... we get x= 3-y....

so the min value for that fixed y is

2y^2 +4y -9.....

we had kept y fixed......now we vary y too to get the least value among all values of y....

so we get at y= -1 , the expression has the min value for all x ,y...........

thus min val= -11......