Question

Find the equation of the line with slope -1 that is tangent to the curve y=1/(x-1) (5 marks: 1 mark for a graph, for general equation of the line, for getting the quadratic and for solving for k for the solution. (Lots of awards for best answer)

Answer 1

define the tangent line in point slope form as:

y - f(c) = f'(c) (x-c)

such that c is the value of x that makes y' = -1