Question 163213
To find the zeros of the function, you need to solve the equation:
{{{(1/2)x^3-x=0}}}
Factoring the left side, we have
{{{x((1/2)x^2 - 1)=0}}}
So
{{{x = 0}}} or {{{(1/2)x^2-1=0}}}
Solving {{{(1/2)x^2-1=0}}}, we obtain:
{{{(1/2)x^2=1}}}
{{{x^2=2}}}
{{{x = sqrt(2)}}} or {{{x=-sqrt(2)}}}
So the zeros of the function are {{{0}}}, {{{sqrt(2)}}} and {{{-sqrt(2)}}}