# What is the equation of the line that is normal to f(x)= x(x-4)  at  x= 5 ?

##### 1 Answer
Mar 7, 2018

#f(x) = x^2-4x

$f \left(5\right) = 25 - 20$

$f \left(5\right) = 5$

$f ' \left(x\right) = 2 x - 4$

$f ' \left(5\right) = 2 \left(5\right) - 4$

$f ' \left(5\right) = 6$

If $6$ is the slope of the tangent, then $\frac{1}{6}$ is the slope of the normal

$y - 5 = \frac{1}{6} \left(x - 5\right)$

$y = \frac{x}{6} - \frac{5}{6} + \frac{30}{6}$

$y = \frac{x}{6} + \frac{25}{6}$

$6 y = x + 25$