What is the equation of the line normal

Bradley Barron

Bradley Barron

Answered question

2022-04-09

What is the equation of the line normal to f(x)=(5x)2 at x=2?

Answer & Explanation

Kapovkah7hpl

Kapovkah7hpl

Beginner2022-04-10Added 14 answers

Given f(x)=(5x)2
f(x)=2510x+x2
Its general slope is given by the derivative:
f'(x)=2x-10
At x=2 this slope will be
2(2)-10=-6
and a line normal to it (i.e. perpendicular to it) will have a slope
=(16)=16
At x=2,f(2)=(52)2=9
giving a point (2,9)
Using the slope-point form for the normal line
y9=16(x2)
We can simplify this as
6y-54=x-2
or (in standard form)
x-6y=-52

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