What is the monotone f(x)=(x^2)/2+1/x ?

The monotone f(x)=(x^2)/2+1/x is Decreasing:-infinity <x<0,Decreasing:0<x<1,Increasing:1<x<infinity

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monotone f(x)=(x^2)/2+1/x

monotone intervals

f (x) = \frac{x ^{2}}{2} + \frac{1}{x}

Decreasing : - \infty < x < 0, Decreasing : 0 < x < 1, Increasing : 1 < x < \infty

Solution steps

f^{'} (x) = x - \frac{1}{x ^{2}}

Find intervals:

Decreasing

: - \infty < x < 0,

Decreasing

: 0 < x < 1,

Increasing

: 1 < x < \infty

Decreasing : - \infty < x < 0, Decreasing : 0 < x < 1, Increasing : 1 < x < \infty

What is the monotone f(x)=(x^2)/2+1/x ?
The monotone f(x)=(x^2)/2+1/x is Decreasing:-infinity <x<0,Decreasing:0<x<1,Increasing:1<x<infinity