Value of $f'(6)$ in given polynomial 
A polynomial function $f(x)$ of degree $5$  with leading coefficients one $,$ increase in the interval
$(-\infty,1)$ and $(3,\infty)$ and decrease in the interval $(1,3).$ Given that $f'(2)=0\;, f(0)=4$
Then value of $f'(6) =$

Attempt: Given function increase in the interval $(-\infty,1)$ and $(3,\infty)$ and decrease
in the interval $(1,3).$ So we have $f'(1)=0$ and $f'(3)=0$
So $f'(x) = (x-1)(x-2)(x-3)(x-\alpha)$
Could some help me how i calculate $\alpha,$ thanks

just a hint
$$f (x)=x^5+ax^4+bx^3+cx^2+dx+4$$
$$f'(2)=80+32a+12b+4c+d=0$$
$$f'(1)=5+4a+3b+2c+d=0$$
$$f'(3)=405+108a+27b+6c+d=0$$
$$f'(6)=5.6^4+4.6^3.a+3.6^2b+12c+d $$
