Investigate the given two parameter family of functions

Question

Question: Investigate the given two parameter family of functions. Assume that a and b are positive.

(a) Graph f(x) using b = 1 and three different values for a.

(b) Graph f(x) using a = 1 and three different values for b.

(c) In the graphs in parts (a) and (b), how do the critical points of f appear to move as a increases? As b increases?

(d) Find a formula for the x-coordinates of the critical point(s) of f in terms of a and b.

f(x) = ax/(x² + b)