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

1 Answer
Jan 16, 2017

Answer:

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]}