Clicky Clicky

I am unable to determine the co-ord of C... well I get a value but it doesnt look right, I get $\displaystyle (1 ; 0) $ which does not seem to fit the value of C. All the other values seem to be perfect execpt for C. Here are my workings.

14.1) $\displaystyle f(x) = (x-2)^2(2x-1)=0 $

$\displaystyle (x^2-4x+4)(2x-1)=0 $

$\displaystyle 2x^3-9x^2+12x-4=0 $

$\displaystyle A = y-intercept$

$\displaystyle y=-4 (0 ; -4) $

$\displaystyle B = (2x-1) $

$\displaystyle x = 1/2 $

$\displaystyle (1/2 ; 0) = B $

$\displaystyle C = f(x) = 2x^3-9x^2+12-4 $

$\displaystyle f'(x) = 6x^2-18+12

x^2-3x+2=0 $

$\displaystyle (x-1)(x-2)=0 $

$\displaystyle f(1) = 6(1)^2-18(1) +12 = 0 $

$\displaystyle C=( 1; 0)$

$\displaystyle f(2) = 6(2)^2-18(2)+12=0 $

$\displaystyle (2;0) = D $ Which can also be taken from $\displaystyle (x-2) $

Either the book is incorrect or I am. The book has been incorrect a few times so ye :/