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

The inflection f(x)=(x^2)/2+1/x is (-\sqrt[3]{2},0)

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

inflection

(- 32, 0)

Solution steps

f^{''} (x) = 1 + \frac{2}{x ^{3}}

Find intervals:

Concave Upward

: - \infty < x < - 32,

Concave Downward

: - 32 < x < 0,

Concave Upward

: 0 < x < \infty

Plug

x = - 32

into

\frac{x ^{2}}{2} + \frac{1}{x} : 0

(- 32, 0)

What is the inflection f(x)=(x^2)/2+1/x ?
The inflection f(x)=(x^2)/2+1/x is (-\sqrt[3]{2},0)