y = 1/a+4a+ 1/2≥2√[( 1/a)(4a)]+ 1/2 = 9/2

If and only if 1/a=4a, that is, a= 1/2, y takes the minimum value of 9/2.

(2) when a < 0, y =1/a+4a+1/2 ≤-2 √ [(1/a) (4a)]+1/2 =-3/2.

If and only if a=- 1/2, the maximum value of y is -3/2.

To sum up, this function has no minimum value.

The value range of this function is (-∞, -3/2]∩[9/2,+∞).