Does $f(x)=(x-2)^{\frac{2}{3}}(2x+1)$ have Point of Inflection Does $$f(x)=(x-2)^{\frac{2}{3}}(2x+1)$$ have Point of Inflection
I differentiated it twice, getting
$$f''(x)=\frac{10(2x-5)}{9 (x-2)^{\frac{4}{3}}}=0$$
which implies $$x=2.5$$ is Point of Inflection.
But it is unnoticeable in Graphing calculator?

As mentioned in the comments, it is difficult to notice just by looking at the graph of the second derivative, but $2.5$ really is a point of reflection, as your correctly differentiated function shows. 
If you instead plot the derivative of the function, you will perhaps get more convinced even graphically (since it is clear that the first derivative is decreasing upto (approximately) $2.5$, and increasing after):

