# Thread: Families of Curves

1. ## Families of Curves

A family of functions is given by

Find values of a and b so that the function r has a local minimum at the point (5 , 9)

Find the vertical asymptotes of r with the values of a and b found in part (a).

ok can someone just help me start this one...it would help alot, thanks

mathaction

2. Originally Posted by mathaction
A family of functions is given by

Find values of a and b so that the function r has a local minimum at the point (5 , 9)
I give you two hints:

first, given that (5,9) is on the graph it means that:

r(5) = 9 ............(1)

secondly, since at x = 5 we have a minimum, it means that r'(5) = 0 ........(2)

thus you will obtain two simultaneous equations where you can solve for the two unknowns

Find the vertical asymptotes of r with the values of a and b found in part (a).
this part is trivial once you've completed the first part. just find the x's that make the denominator zero.