What is the equation of the normal line at x = 2 on the curve y = x^2 - 4x + 3

Expert Answers
sciencesolve eNotes educator| Certified Educator

You need to remember that the equation of normal line to a curve means that the line is perpendicular to the tangent line to the curve. You should remember that the tangent line to a curve at a point expresses the derivative of function at the tangency point.

You need to find the derivative of function `f(x) = x^2 - 4x + 3`  such that:

`f'(x) = 2x - 4`

You need to find value of derivative at x=2 such that:

`f'(2) = 2*2 - 4 =gt f'(2) = 0`

Notice that the tangent line to the curve at `x = 2`  is parallel to x axis since f'(2) = 0, hence the normal line to the tangent line is parallel to y axis and it passes through `x = 2` .

Hence, the equation of the normal line  to the curve `y = x^2 - 4x + 3`  at x = 2.