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

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Answer 1 · 2018-03-07T13:50:14

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

$f(5) = 25-20$

$f(5) = 5$

$f'(x) = 2x-4$

$f'(5) = 2(5) -4$

$f'(5) = 6$

If $6$ is the slope of the tangent, then $1/6$ is the slope of the normal

$y-5 = 1/6(x-5)$

$y=x/6-5/6+30/6$

$y=x/6+25/6$

$6y=x+25$

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