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

Jun 2, 2018

$x \approx 0.8433440445$

#### Explanation:

we get

$f ' \left(x\right) = - \sin \frac{x}{x} ^ 2 - 2 \cos \frac{x}{x} ^ 3 + 6 {x}^{2} + 1$
so $f ' \left(x\right) = 0$
if
$6 {x}^{5} - {x}^{3} - x \sin \left(x\right) - 2 \cos \left(x\right) = 0$
using a numerical method we get
$x \approx 0.8433440445$