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

1 Answer
Aug 1, 2017

y = -x+3

Explanation:

First find the equation of the line TANGENT to the function at the point; then find the equation of the line that passes through that point but has a perpendicular slope.

f(x) = x^2-x+2

f(1) =1^2-1+2 = 2

f'(x) = 2x -1

f'(1) = 2(1) - 1

f'(1) = 1

We now have the point and the slope of the line tangent to f(x) at x=1.
color(blue)("Tangent line: " y = 1(x-1)+2)

Simplified tangent line: y=x+1
Since the slope is 1, the slope of the normal line will be frac{-1}{1} = -1

color(blue)("Normal line: " y = -1(x-1) + 2)

Simplified normal line:
y = -x+1+2

y = -x+3

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