1. Derive f' (x) = 3x 2-6x+6 = 3 (x 2-2x+2) > 0, so f(x) is a monotonically increasing function, the maximum value is f( 1)=2, and the minimum value is.

f(- 1)=- 12

2. because the cost of producing x products is c=25000+200x+( 1/40)x? ,

So the average cost is f (x) = c/x = 25000/x+200+(1/40) x,

Derive f' (x) =-25000/x 2+( 1/40), make f'(x)=0 and get x= 1000.