Find the Minimum

Solution

Write f(x) as follows:

f(x)	= 12 +	18x4 - 12x2 + 2
		x2
	= 12 +	2(9x4 - 6x2 + 1)
		x2
	= 12 +	2((3x2 - 1)/x)2

From this form, it's clear that the minimum value of f(x) is 12.