There is only one stationary point for the function
y(x)=((x-1)^(1/3))*((x+2)^(2/3)) and it is pointwith coordinates
x=0 and y=-1.5859
At first, first derivation is
y'(x)=x/((x-1)^(2/3))*((x+2)^(1/3)) and we obtained that
y'(0)=0. Then we can find second derivation of the function and for value x=0 we could concluded that
y''(0)>0. In this stationary point it is minimum value of the function.
Finally, at the points x=-2 and x=1 we have so called
critical values for this function.
See captured images below
1. Second derivation for y(x)
2. Graph y(x)
3. Enlarged detail of the graph y(x)
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