Given:
a,b,c >0 and a+b+c=1 ;
P=(1/a)+(2/b)+(3/c);
1)Find the minimum value of P;
2)Does P have maximum value ?
(In reply to
A better way to solve this ! by vohonam)
I'm not familiar enough with (or I've forgotten) how you can prove a minimum or maximum using Cauchy's inequality (or any inequality, really). Regardless, though, I'd argue that using a Lagrange multiplier is very easy in this particular case. The gradients are trivial to calculate, and the multiplier itself just drops right out of the picture.
re: A better way to solve this !
