This topic mainly examines the knowledge of finding the maximum value by using derivative tangent equation and monotonicity of judgment function, and examines the application ability and operation ability of transformation and classification discussion ideas.

The first question is to use derivatives to find the magnitude of extreme points, f(-2), f(- root number 2/2) and f (root number 2/2). And f (1).

Solution: (1) From f (x) = 2x 3, f' (x) = 6x 2-3, let f'(x)=0, and get x- radical number 2/2 or x= radical number 2/2, because the detailed answer is here. Lal function f (x) = 2x 3-3x.

(i) Find the maximum value of f(x) in the interval [-2, 1];

(2) If there are three straight lines tangent to the curve y=f(x) at the intersection P( 1, t), find the range of t;

(3) The questions I asked A (- 1, 2), B (2, 10) and C (0, 2) are that how many straight lines are tangent to the curve y=f(x). This question is still very difficult (just write the conclusion). I didn't have any ideas at first. I didn't understand until I read the answer. Let's go