Respuesta :

gmany

The zeros of function are x-s, for which f(x) = 0:

[tex]f(x)=\dfrac{1}{2}x^3-x\\\\f(x)=0\iff\dfrac{1}{2}x^3-x=0\ \ \ \ |\cdot2\\\\x^3-2x=0\\\\x(x^2-2)=0\iff x=0\ \vee\ x^2-2=0\\\\x=0\ \vee\ x^2=2\\\\\boxed{x=0\ \vee\ x=-\sqrt2\ \vee\ x=\sqrt2}[/tex]