Question $3.(11$ points $=5+6)$ Given is the function $f(x)=x^{\frac{2}{3}}(3-x{)}^{\frac{1}{3}},$xinR.

a$)$ Show with the limit definition of differentiability that $f(x)$ is differentiable at $x=1.$

b$)$ Show with clear steps that $f^{\text{'}\text{'}}(x)=\frac{-2}{x^{\frac{4}{3}}(3-x{)}^{\frac{5}{3}}}$ and find the coordinates of the inflection point$($s$).$