# What is the equation of the line normal to  f(x)=x(x-2)  at  x=2?

Jul 9, 2017

$2 y = 2 - x$

#### Explanation:

$f \left(x\right) = {x}^{2} - 2 x \implies f ' \left(x\right) = 2 x - 2 \implies f ' \left(2\right) = 2 \cdot 2 - 2 = 2$

The normal slope is $- \frac{1}{2}$ and it passes through $\left(2 , f \left(2\right)\right)$

$f \left(2\right) = {2}^{2} - 2 \cdot 2 = 0$

The wanted normal is $g \left(x\right) = - \frac{1}{2} \left(x - 2\right)$