What is the equation of the line normal to  f(x)=(x^2-x)(x-2)  at  x=1?

Sep 11, 2016

$y = x - 1$

Explanation:

Equation of the line normal is $- y {'}_{0} \left(y - {y}_{0}\right) = x - {x}_{0}$

$y ' = \left(2 x - 1\right) \left(x - 2\right) + {x}^{2} - x = 3 {x}^{2} - 6 x + 2$

y'_0=-1; y_0=0; x_0=1

$- \left(- 1\right) \cdot \left(y - 0\right) = x - 1$