This topic mainly investigates the knowledge of using derivative tangent equation and monotonicity of judgment function to find the maximum value, and investigates the application ability and calculation ability of transformation and classification discussion ideas. The answer is/exercise/math /804 130, which is still very difficult.

The function f (x) = 2x 3-3x is known.

(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;

(iii) How many straight lines are tangent to curve y=f(x) at points A (- 1 2), B(2 10) and C (0 0,2)? (Write conclusions only)