The monotone interval and extreme value of a function can be obtained by derivation. To solve the range problem, it is often necessary to carry out equivalence transformation and classification discussion.

This question is very difficult and comprehensive. The answer is here/exercise/math /804204. The function f (x) = x 2-2/3ax 3 (a > 0), and x belongs to R ..

(1) Find the monotone interval and extreme value of f(x);

(2) If any x 1 belongs to (2, +∞), there is x2 belonging to (1, +∞), so that f(x 1)×f(x2)= 1 can find the range of a. I hope it can be adopted, and I wish you progress in your study ~