What is the equation of the line normal

daurialebraslmc

daurialebraslmc

Answered question

2022-04-09

What is the equation of the line normal to f(x)=6x3+2x at x=3?

Answer & Explanation

gsmckibbenx7ga

gsmckibbenx7ga

Beginner2022-04-10Added 17 answers

Given -
y=6x3+2x
dydx=18x2+2
Slope, exactly at x=3
At x=3;18(3)2+2=164
This is the slope of the tangent m1=164
Slope of the normal m2=1m1=1164
At x=3;6(3)3+2(3)=162+6=168
We have to find the equation of the line passing through the point (3, 168) with the slope 1164
mx+c=y
1164(3)+c=168
c=168+3164=27552+3164=27555164
y=x164+27555164

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