Families of Curves

[holmdeal]

A family of functions is given by

(a) For what values of a and b does the graph of r have a vertical asymptote? Where are the vertical asymptotes in this case?
(b) Find values of a and b so that the function r has a local maximum at the point

 

[pka]

First of all I would try to graph this using different values for a & b.

Look at \(\displaystyle \L
a < 0\) and the what happens if \(\displaystyle \L
x = b \pm \sqrt { - a}\) !

Can you see local maxima at x=b?