Find the maximum and minimum values of the function f (x) = x + 1 / X in the interval [1 / 2,3]

2,3.33333 (in this interval, x, 1 / X are all greater than 0, we can use the mean inequality. Obviously, when x = 1 / x, that is, x = 1 is f (x) has the minimum value, f (1) = 2;) judging the monotonicity by derivation, it is easy to know that its derivative is 1-1 / x ^ 2, which is obviously a decreasing function on [1 / 2,1], and (1,3] is an increasing function

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