f(x)=x^{2 / 3}(6-x)^{1 / 3}, f^{\prime}(x)=\frac{4-x}{x^{1 / 3}(6-x)^{2 / 3}}, f^{\prime \prime}(x)=\frac{-8}{x^{4 / 3}(6-x)^{5 / 3}} a) Determine the domain, x-intercept(s), and y-intercept. b) Determine the interval(s) on which f(x)

is increasing and those on which f (x) isdecreasing. Justify analytically. c) Determine the interval(s) on which f(x) is concave up and those on which f(x) is concavedown. Justify analytically. d) Identify the coordinates (x, y) of all relative maxima and minima and all inflection points. If there are none, state so.