Question

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

Answer 1

The function has no points of inflection.

Explanation:

Find the points when `f''(x)` switches sign (when `f` switches concavity).

`f'(x)=8-4/x`

`f''(x)=4/x^2`

`f''(x)` 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]}