The graph of g(x)=x`3-x

Question

^graph 

Answer 1

g(x) = x^3 - x

 

       = x(x^2 - 1)

 

       = x(x+1)(x-1)

 

 zeros at x=0, x=1, x=-1

 

sign table for

 

x<-1  --> negative

-1 < x < 0 ---> postiive

0 < x < 1  ---> negative

x>1 ---> positive

 

(-sqrt(3)/3 / 0.3849 ) are ( sqrt(3)/3 , -0.3849) are the relative max and min points

 

www.desmos.com used to graph functions