Monotone interval and extremum of G (x) = x ^ 3-6x

Monotone interval and extremum of G (x) = x ^ 3-6x

After derivation, G '(x) = 3x ^ 2-6
Let 3x ^ 2-6 > = 0, x > = √ 2 or X

It is known that the cubic function f (x) = X3 + AX2 + BX + C takes the extremum when x = 1 and x = - 1, and f (- 2) = - 4. (1) find the expression of function y = f (x); (2) find the monotone interval and extremum of function y = f (x)

(1) F (x) = X3 + AX2 + BX + C, f ′ (x) = 3x2 + 2aX + B; then from the meaning, f ′ (1) = 3 + 2A + B = 0f ′ (− 1) = 3 − 2A + B = 0f (− 2) = 8 + 4A − 2B + C = − 4, the solution is a = 0, B = - 3, C = - 2, so f (x) = x3-3x-2, (2) from (1), f ′ (x) = 3x2-3 = 3 (x +

How to judge whether the signs of the derivatives on the left and right sides of the extremum are the same when using the derivative to find the extremum?
Do you bring in a number at random, or is there any other rule to follow?
Sometimes it's troublesome to carry in numbers to evaluate
thank!

Extremum has nothing to do with positive and negative, it is the number when the reciprocal is zero, not the original function is zero, so we can't find a shortcut here