# What are the points of inflection of f(x)=8x - 4 lnx ?

Dec 23, 2015

The function has no points of inflection.

#### Explanation:

Find the points when $f ' ' \left(x\right)$ switches sign (when $f$ switches concavity).

$f ' \left(x\right) = 8 - \frac{4}{x}$

$f ' ' \left(x\right) = \frac{4}{x} ^ 2$

$f ' ' \left(x\right)$ is always positive (or undefined when $x = 0$), thus the function never switches concavity and has no points of inflection.

graph{8x-4lnx [-40.3, 91.34, -9.45, 56.4]}