We have the following:
[tex]f(x)=(x+2)^{\frac{2}{3}}[/tex]
the first thing is to derive the function:
[tex]f^{\prime}(x)=\frac{2}{3\cdot(x+2)^{\frac{1}{3}}}[/tex]
the critical points are points where the function is defined and its derivative is 0 or it is not defined
[tex]\begin{gathered} 3\cdot(x+2)^{\frac{1}{3}}=0 \\ \frac{3}{3}\cdot(x+2)^{\frac{1}{3}}=\frac{0}{3} \\ (x+2)^{\frac{1}{3}}=0 \\ x+2=0\rightarrow x=-2 \end{gathered}[/tex]
now,we graph and we have
we can see that it is a minimum, therefore the answer is relative minimum (-2, 0)
