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

1 Answer
Jan 10, 2016

y=x/4-19/2

Explanation:

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

m_n=-1/m=-1/(-4)=1/4

The normal line is

(y-y_0)=m_n(x-x_0)

with
x_0=2
y_0=f(x_0)=y(x_0)=-4*2-1=-8-1=-9

then:

the normal line becomes:

(y-(-9))=(1/4)(x-2)

y+9=1/4x-1/2
y=x/4-1/2-9=x/4-((1+18)/2)=x/4-19/2