Find the x-coordinates of the points on the curve y=2x^3+3x^2−12x+5 where the tangent is horizontal.

List these x-coordinates

Question

Find the x-coordinates of the points on the curve y=2x^3+3x^2−12x+5 where the tangent is horizontal.

List these x-coordinates

anonymous · Answer

So you are pretty much trying to find when it crosses the x axis.

anonymous · Answer

And have you done derivatives yet.

anonymous · Answer

umm yeah i think i just need an explanation of how to start no i haven't taken the derivative yet

anonymous · Answer

so for the derivative i got 6x^2+6x-12

anonymous · Answer

well the slope of the line to start off is the first derivative so its pretty simple you would get y'=6x^2+6x-12
to find when the tangent is horizontal is when the slope=0 
so you want to set the first derivative = 0 and solve for you x values.

anonymous · Answer

its a degree 2 so you have to have 2 solutions I have got 2 answers for x. 
Now you have to find your y values which you should plug your x coordinate into that original y equation and then it will give you the matching y coordinate.

anonymous · Answer

my two values for x are -2,1 i think thats all i need thank you :)

anonymous · Answer

yeap now you just plug it back into the original equation to get your y coordinates.