Thread: family of functions- verticle asymptotes

im stuck on a question!

a family of functions is given by:
r(x)=1/a+(x-b)^2

a) for what vales of a and b does the graph of r have a verticle asymptote? where are the verticle asymptotes in this case?
b) find values of a and b so that the function r has a local maximum at the point (3,5)

any help would be greatly appreciated
thanks

Hello,

I'm not sure what you mean:



or

the second one!

Have you tried solving a + (x - b)^2 = 0? I think that would pin it down for you.

Originally Posted by Paige05

im stuck on a question!

a family of functions is given by:
r(x)=1/(a+(x-b)^2)

a) for what vales of a and b does the graph of r have a verticle asymptote? where are the verticle asymptotes in this case?
b) find values of a and b so that the function r has a local maximum at the point (3,5)

A function has vertiacal asymptotes if the denominator equals zero:



That means:

you get no vertical asymptote if a > 0

you get exactly one vertical asymptote if a = 0 then the equation of the asymptote is : x = b

you get 2 vertical asymptotes if a < 0. The equations of the asymptotes are:


to b):

Use chain rule to derivate:

Rearrange:





From your problem you know that now b = 3. Calculate

ahhhhh.... i see!
thanks so much