plz check: find distance between critical number of f(x)

[Guest]

find distance between two critical numbers of the function f(x)=x^3-3x+27.
(a)1 (b)8 (c)3 (d)2 (e)none

my work::
f(x)=x^3-3x+27
f'(x)= 3x^2-3
f ' (x)=0
3x^2-3=0
x^2=1
x=+/- 1
now critical points are f(1)=25 so (1,25)
f(-1) =29 so (-1,29)

Now the distance formula sqrt[(x2-x1)^2+(y2-y1)^2] =sqrt[(-1-1)^2+(29-25)^2]=sqrt[4+16]=sqrt[20]

the answer doesnot match with given answers....

 

[galactus]

One of the choices is 'none', isn't it?. It isn't 1, 8, 3, 2. So, process of elimination tells us...................?.