Mathematics - Application of Derivative Question with Solution | TestHub

Write $p(t)=C(t-1)(t-3)(t-5)(t-r)$. If $r=7$, then $p\prime (7)=C(6)(4)(2)\ne 0$, so $r\ne 7$. Hence $p\prime (7)/p(7)=1/6+1/4+1/2+1/(7-r)=0$. The first three terms sum to $11/12$, giving $7-r=-12/11$ and $r=89/11$. Thus $11x=89.00$.