Question

What are the local extrema of `f(x) = tan(x)/x^2+2x^3-x`?

Answer 1

Near `+-1.7`. See graph that gives this approximation. I would try to give more precise values, later.

Explanation:

The first graph reveals the asymptotes `x = 0, +-pi/2 +-3/2pi, +-5/2pi, ..`

Note that `tan x/ x^2=(1/x)(tanx/x)`

has the limit `+-oo`, as `x to 0_+-`

The second (not-to-scale ad hoc ) graph approximates local extrema

as `+-1.7`. I would improve these, later.

There are no global extrema.
graph{tan x/x^2+2x^3-x [-20, 20, -10, 10]}
graph{tan x/x^2+2x^3-x [-2, 2, -5, 5]}