In your post g'(x) calculation is incorrect. In case you want to verify see the solution below.
Spoiler:
only def for
find the highest and lowest value for .
Attempt: https://dl.dropbox.com/u/586465/Phot...2 09 04 42.jpg
I find (0,0) and (±√4 ; ±2/3*√6)
The book says the answer is: Skärmavbild 2012-09-12 kl. 09.08.23.png