Find the critical points of f(x)=x2/3(x−5)f(x) = x^{2/3}(x-5)f(x)=x2/3(x−5) and classify them.
Critical points at x=0x=0x=0 (no extremum — cusp) and x=2x=2x=2 (local min)
Critical point at x=2x=2x=2 only (local min)
Critical points at x=0x=0x=0 (local max) and x=2x=2x=2 (local min)
Critical point at x=5x=5x=5 (global min)