Home > Calculus > Normal Line to a Tangent

What is the equation of the line normal to #f(x)=6x^2 + 4x - 9 # at #x=1#?

Answer 1

Ezekiel Alexander

#x+16y-17=0#. See the normal-inclusive Socratic graph.

y at x = 1 is 1. So, the foot of the normal is P(1, 1).

y'=12x+4=16, at P.

The slope of the normal #= -1/(y')=-1/16#.

So, the equation to the normal at P(1, 1) is

#y-1=-1/16(x-1)#, giving

#x +16y-17=0#.

graph{(6x^2+4x-9-y)(x+16y-17)((x-1)^2+(y-1)^2-.1)=0 [-22, 22, -11, 11]}

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Samantha Adkison

The equation of the line normal to f(x)=6x^2 + 4x - 9 at x=1 is y = -12x + 17.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.