Let f be the function defined by fx kx x ( ) = - ln for x > 0, where k is a positive constant.

(a) Find f ¢( ) x and f ¢¢( ) x .

(b) For what value of the constant k does f have a critical point at x = 1 ? For this value of k, determine

whether f has a relative minimum, relative maximum, or neither at x = 1. Justify your answer.

(c) For a certain value of the constant k, the graph of f has a point of inflection on the x-axis. Find this value

of k.