Let g (x) = lnf (x) = xlnx+(1-x) ln (1-x) g` (x) =1+lnx-1-ln (1-ln)

When 0

Therefore, the minimum value f( 1/2)= 1/2 is obtained at x= 1/2.

If f(x) monotonically increases (decreases), then lnf(x) monotonically increases (decreases). This is done for the convenience of deduction.

Classification:

The stable value of a function, that is, the maximum or minimum value. The extreme point can only be obtained at the point where the function does not take derivative or the derivative is zero. The highest or lowest values of climatic elements observed in a given period, or in a month or season of that period. If this period is the whole period with observed data, this extreme value is the absolute extreme value.