What is the equation of the normal line

Efrain Watkins

Efrain Watkins

Answered question

2022-04-08

What is the equation of the normal line of f(x)=-4x-1 at x=2?

Answer & Explanation

Austin Sherman

Austin Sherman

Beginner2022-04-09Added 12 answers

If the excercise does not clearly request the derivation use, you could also think:
y=-4x-1
is a line, then the tangent line to it is the line itself
y=mx+q
with
m=-4
and q=-1
mn=1m=14=14
The normal line is
(yy0)=mn(xx0)
with
x0=2
y0=f(x0)=y(x0)=421=81=9
then:
the normal line becomes:
(y(9))=(14)(x2)
y+9=14x12
y=x4129=x4(1+182)=x4192

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