Hello,
I'm not sure what you mean:
or
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
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