What is the equation of the normal line

Jaylyn Villarreal

Jaylyn Villarreal

Answered question

2022-04-07

What is the equation of the normal line of f(x)=x42x35x2+3x+3 at x=1?

Answer & Explanation

madking711kzcb

madking711kzcb

Beginner2022-04-08Added 9 answers

As f(x)=x42x35x2+3x+3 and at x=1 its value is
-1-2-5+3+3=-2 and hence curve passes through (1, -2) and we
need to find equation of normal at this point.
Slope of tangent is given by function's derivative. It is
f(x)=4x36x210x+3 and at x=1 slope is -4-6-10+3=-17.
Hence the slope of tangent is -17 and as normal is perpendicular to it, slope of normal would be 117.
Now using point slope form, equation of normal is
(y+2)=117(x1) or 17y+34=x-1 or
x-17y-35=0

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