There is a graph of a function that looks like y = x^4 , but it has a vertical asymptote at x = -2 and x = 4.

Question

There is a graph of a function that looks like y = x^4 , but it has a vertical asymptote at x = -2 and x = 4.

The question then asks us to arrange the following numbers in decreasing order:

g'(1), g'(-2), g'(0), g'(2), g'(4)

I figured out all of the slopes, but I don't know what to do for g'(-2) and g'(4) because there are vertical asymptotes. The graph can't actually touch -2 or 4 so would both of them be increasing or decreasing?

Answer 1

clearly, since there are asymptotes there, g' is undefined. It might be increasing or decreasing near the asymptote, but g'(-2) and g'(4) are undefined.