I'm not sure if I posed the question correctly but the problem is: find the x coordinates of the points onthe graph of y=x^3-6x^2-15X+1 where the tangent lines are horizontal ?

First step:

Take the derivative which is 3x^2-12x-15

Second step:

Set the equation to zero (because that is the slope of the horizontal line)

Third Step:

What am I solving for ?

LOST !!!!

I tried to graph it in my calculator and draw the tangent lines to get a clue but no such luck