If $f\left(x\right)=(x-2)(x-3)(x-4)(x-5)(x-6)$ then 

If $f\left(x\right)=(x-2)(x-3)(x-4)(x-5)(x-6)$

so, by Rolle's theorem applied on [2, 3], [3, 4], [4,

5], [5, 6] there are $x_1\in (2,3),x_2\in (3,4),x_3\in (4$

$\text{ 5), }{x}_4\in (5,6)$such that $f^{\mathrm{\prime }}\left(x_i\right)=0,i=1,2,3,4\text{. }$

Since $f\text{'}$ is polynomial of degree 4 so cannot have five roots