Home > Calculus > Normal Line to a Tangent

What is the equation of the normal line of #f(x)=x^2-x+5# at #x=2#?

Answer 1

#y=(23-x)/3#

Differentiate:
#f prime(x)=2x-1#
#f prime(2)= 2(2)-1#
#=3#
Therefore the normal has gradient #-1/3# because "#m_1m_2=-1#"for perpendicular lines.
Therefore the equation of the normal line is #y=-x/3+c#.
This has to pass through the point #(1,f(2))#, that is, #(1,7)#.
Therefore #7=-2/3+c# hence #c=23/3#.
So the line is #y=-x/3+23/3#.

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

Answer 2

Paisley Johnson

The equation of the normal line of f(x)=x^2-x+5 at x=2 is y = -3x + 9.

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.