Answer
(a) $x=0,-\sqrt 3,\sqrt 3$ (multiplicity 1).
(b) crosses the x-axis at $x=0,\pm\sqrt 3$.
(c) $2$.
(d) $y=4x^3$.
Work Step by Step
(a) Given $f(x)=4x(x^2-3)=4x(x+\sqrt 3)(x-\sqrt 3)$, we can find zero(s) $x=0,-\sqrt 3,\sqrt 3$ (multiplicity 1).
(b) The graph crosses the x-axis at $x=0,\pm\sqrt 3$.
(c) The maximum number of turning points on the graph is $n-1=3-1=2$.
(d) The end behavior is similar to those of $y=4x^3$.
