Suppose f(x)=g(x)+h(x)

The most important condition for finding the maximum value of a function with basic inequality is that the function g(x)*h(x) is a constant value, and both of them are greater than 0.

Let g (x) = x and h (x) =1/x (x >; 0), then g(x)*h(x) is a constant 1, then f (x) = x+1/x > =2, the minimum value of f(x) is 2.

Suppose g (x) = x, h (x) = x+ 1, (x >；; -1) then we can get f (x) = x+(x+1) > = 2 √ x (x+1),

At this time, the function f(x) jumps to another function, so you can't find the maximum value with the basic inequality. This method uses basic inequalities to enlarge and narrow, and is generally used in some college entrance examination finale questions.