# How do you find points of inflection and determine the intervals of concavity given #y=x^(1/3)(x-4)#?

##### 1 Answer

Jan 8, 2018

There is a point of inflection at

#### Explanation:

Let's say

This means:

and

Points of inflection occur where f''(x) crosses the x-axis, which happens where f''(x) = 0, and there isn't a double root.

In the case of this problem, this occurs at

By substituting numbers around 2, we can easily see that

Therefore, your answer is: