It is more fun to try to prove this inequality without calculus but if you want to use calculus I would start with Lagrange Multipliers.
Using calculus and reasoning prove how, step by step, the following is true.
a, b, and c are >= 0
If a^2 + b^2 + c^2 + abc = 4 show that ab + bc + ac - abc <= 2
This is a calc 3 problem, vectors and planes in spaces, so i'm thinking i have to find the plane for the first equation and then show relationships to the other inequality. Basically, I'm pretty much lost and have no clue where to start. Any help is appreciated. Thanks.
so what would i use as f and g? so would I the gradient of the first equations and set it equal to the gradient of the second, times lamba, and then what? I know how to use lagrange multipliers, but how do you use them in order to prove an inequality? I also made a mistake originally, the equation is suppose to be: a^2 + b^2 + c^2 +abc = 4