George Saliaris
Junior Member
- Joined
- Dec 15, 2019
- Messages
- 53
Find the minimum value of
G(a, b) = (a-2b) ^2 + ( ln((e^a) +1)- b)^2
for the various values of a, b Ε R
A little bit of backround. : I was given some conditions which led to finding a function f(x) = ln(( e^x) +1),I had to prove that f(x) >= 1/2 x +ln2... Anyway.. Can't I just use some transformed inequality of x^2 +y^2 >= 2xy and find the minimum value of G(a,b) in terms of a, b.. Is there something that I am missing?
G(a, b) = (a-2b) ^2 + ( ln((e^a) +1)- b)^2
for the various values of a, b Ε R
A little bit of backround. : I was given some conditions which led to finding a function f(x) = ln(( e^x) +1),I had to prove that f(x) >= 1/2 x +ln2... Anyway.. Can't I just use some transformed inequality of x^2 +y^2 >= 2xy and find the minimum value of G(a,b) in terms of a, b.. Is there something that I am missing?