# What is the equation of the normal line of f(x)=x/(x-1)  at x=4 ?

Jan 15, 2018

derivative for slope , use 2 point form of a line

#### Explanation:

${f}^{'} \left(x\right) = \frac{\left(x - 1\right) - \left(x\right)}{x - 1} ^ 2$ = $- \frac{1}{x - 1} ^ 2$

hence slope of normal is

${\left(x - 1\right)}^{2}$ by $m 1. m 2 = - 1$ ( tangent perpendicular to normal )

find value of $y \left(\mathmr{and} f \left(x\right)\right)$ @ $x = 4$
$y = \frac{4}{3}$
and value of slope is $9$

by 2 point form

$y - \frac{4}{3} = 9 \left(x - 4\right)$

hence normal equation is:
$3 y - 27 x = - 104$ or $27 x - 3 y = 104$

hope u find it helpful :)