(1) f'(x) = 6x^2 - 6ax
f'(1) = 6 -6a
y = -x/3 + 1的斜率k = -1/3
f(x)在点(1,f(1)）处的切线与y= -x/3 +1垂直,此切线的斜率= -(-1/3) = 3
f'(1) = 6 -6a = 3
a = 1/2
f(x) = 2x^3 -3x^2/2 +2
f'(x) = 6x^2 - 3x = 3x(2x -1)
x < 0:2x - 1 < 0,x(2x -1) > 0,f(x)递增
0 < x < 1/2:x > 0,2x -1 < 0,x(2x -1) > 0,f(x)递减
x > 1/2:x > 0:2x - 1 > 0,x(2x -1) > 0,f(x)递增