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

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Answer 1 · 2017-07-09T13:52:49

$2y = 2-x$

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

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

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

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

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