If a+2b+c=4,then what is the maximum value of ab+bc+ac?

First,

c=4-a-2b......(1),then

substute it in ab+bc+ca.........(2)

now differentiate this equation 2 times first wrt a and then wrt b.

now that you have two equations, solve them using linear equations in two variables and get values for a and b.since you got those answers after differentiating them, you have their greatest values. now get the value for c using eqn (1).now again substute all the values in (2) and you thus have its greatest value.