Let $f(x)=3x^{\frac{2}{3}}-2$

$($a$)$ Find the first and second derivatives of $f.$

$($b$)$ Find the critical points of $f.$

$($c$)$ Complete a First Derivative Sign Chart of $f.$

$($d$)$ Classify the critical points as a either relative minima, relative maxima, or neither.

$($e$)$ Complete a Second Derivative Sign Chart of $f.$

$($f$)$ Find the open intervals on which $f$ is concave down.

$($g$)$ Identify any inflection points of $f.$