What is the equation of the normal line of #f(x)=x^2-4x# at #x=1#?
A normal line is a perpendicular line. In order to find it at a certain point, we need to find the tangent line at that point, and then find the line passing through that point whose slope, multiplied by the slope of the tangent line, is equal to
The slope of the tangent line at a point is given by the derivative of the function, evaluated at that point.
Thus the slope of the tangent line of
The equation of a line with slope
As we are looking for the normal line at
Putting this together with the slope gives us
Thus the equation of the normal line is