Question

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

Answer 1

`2y = 2-x`

Explanation:

`f(x) = x^2 - 2x => f'(x) = 2x - 2 => f'(2) = 2 * 2 - 2 = 2`

The normal slope is `-1/2` and it passes through `(2, f(2))`

`f(2) = 2^2 - 2 * 2 = 0`

The wanted normal is `g(x) = -1/2 (x - 2)`