What is the equation of the normal line

Miguel Hanson

Miguel Hanson

Answered question

2022-04-09

What is the equation of the normal line of f(x)=x38x2+9x3 at x=-1?

Answer & Explanation

pobijedi6wro

pobijedi6wro

Beginner2022-04-10Added 15 answers

f(-1)=-21
f(x)=3x216x+9
f(1)=3+16+9=28=mtan
The slope of the normal line at x=-1 is the negative reciprocal of the slope of the tangent line m=28 which would be 128.
So, using a slope formula:
yy1=m(xx1)
We get:
y+21=128(x+1)
y=128x58928

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