Relative extrema?

Question

Find all relative extrema of the function. Use second derivative test if applicable.

f(x) = x/x^2 - 1

Note: There are no endpoints

Answer 1

Is your function f(x) = x/(x^2 - 1)? If so, the derivative is
f'(x) = -(x^2 + 1)/(x^2 - 1)^2. The derivative is always negative, except at x = +/-1, where the function is not defined. Therefore, the function is always decreasing, so has no extrema.