Hello, ^_^Engineer_Adam^_^!
Plot the graph of the function and from the graph, estimate the point of inflection
and where the graph is concave upward and concave downward.
Confirm your estimates analytically.
. . $\displaystyle f(x) = (x + 2)^{\frac{1}{3}}$ I used an "eyeball" approach to graph it.
We have: .$\displaystyle y \:=\:(x + 2)^{\frac{1}{3}}\quad\Rightarrow\quad x \:=\:y^3  2$
This is a "sideways" cubic with its vertex at (2,0). Code:

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It appears that it is concave up for $\displaystyle x < 2$ and concave down for $\displaystyle x > 2$.
We have: .$\displaystyle f'(x) \:=\:\frac{1}{3}(x + 2)^{\frac{2}{3}}$
Then: .$\displaystyle f''(x)\:=\:\frac{4}{9}(x + 2)^{\frac{5}{3}} \:=\:\frac{4}{9(x+2)^{\frac{5}{3}}} $
At $\displaystyle x = \text{}2\!:\:f''(2)$ is undefined.
For $\displaystyle x < \text{}2\!:\;f''(\text{}3) \:=\:\frac{4}{9(\text{}1)^{\frac{5}{3}}} \:=\:+\frac{4}{9}$ . concave up: $\displaystyle \cup$
For $\displaystyle x > \text{}2\!:\;f''(\text{}1) \:=\:\frac{4}{9(1)^{\frac{5}{3}}} \:=\:\frac{4}{9}$ . concave down: $\displaystyle \cap$
Therefore: .$\displaystyle \begin{array}{cc}\text{concave up} & \text{on }(\text{}\infty,\,\text{}2) \\ \text{concave down} & \text{on }(\text{}2,\,\infty) \end{array}$