Tangents And Normals

Slope of given line: , so slope = Required slope of tangent = negative reciprocal = Differentiate : Substitute in :

The equation is .
First, differentiate both sides: At the point (1,1), substitute and into the derivative.
We get the slope of the tangent line.
Next, use the point-slope form of the equation of the tangent.
Substitute the point into the equation of the curve to find where the tangent meets the curve again.
This gives .