Finding Tangents and Normals

Question

Find an equation for each tangent to the curve y = 1 / (x-1) that has a slope of -1.

Find an equation for each normal to the curve y = 1 / (x-1) that has a slope of 1.

Answer 1

dy/dx = -1/(x-1)²

It equals -1 when x=2 (and this is a double root so that this is the only place where the derivative equals -1.

The function passes through (2,1) so that the equation of the tangent line is

-1 = (y-1)/(x-2).

The normal has slope 1 and you should be able to find the equation forit.