How do you find the equation of a normal line to a curve at a given point?
The equation of a normal line will have the form
and its slope will be the negative reciprocal of the curve's derivative at the point. That is to say, take the value of the derivative at the point, divide 1 by it, and then multiply that value by
This is much better illustrated with an example:
Let's say that we are expected to find the equation of a line normal to the curve
The negative reciprocal of
The last step is to plug in the coordinates of our point and solve for
Now we have everything needed to put our full equation together: