Question

Consider the function f(x) = x/(x-1)

Are there any turning points? Explain how this could help you graph f(x) for large values of x?

Ans: turning points is another word for checking the concavity, and therefore i find the second derivative and equate it to zero and see where it is concave up and down, using that information i can know when the graph is increasing or decreasing, with its end behaviors near the asymptote

Answer 1

Correct.
Did you find any turning points?

Answer 2

I get the second derivative as f''(x) = 2/(x-1)^3. If f''(x) = 0 then there are no solutions, hence there are no turning points.

Am i correct? But how does that help me graph f(x) for large values.