Question 881138
Tangent line is horizontal means the value of the derivative is zero since the derivative is the value of the slope of the tangent line.
Take the derivative and set it to zero.
{{{df/dx=3x^2-12}}}
{{{3x^2=12}}}
{{{x^2=4}}}
{{{x=0 +- 2}}}
.
.
.
{{{drawing(300,300,-5,5,-25,25,circle(-2,15,0.25),circle(2,-17,0.25),blue(line(-20,15,20,15)),blue(line(-20,-17,20,-17)),graph(300,300,-5,5,-25,25,x^3-12x-1))}}}