For what values of x does the graph of F9x) = 2x^3 - 3x^2 + 12x + 87 have a horizontal tangent?

Answer 1

this is the same as asking where F'(x) = 0

Since F'(x) = 6x^2-6x+12

where would that be?

Answer 2

6x4=24
2x6=12+12=24

so...2?

Answer 3

No, it's almost a trick question.
6x^2-6x+12 is never zero (has no real roots)

So, F(x) never has a horizontal tangent.
Visit wolframalpha.com and type in

2x^3 - 3x^2 + 12x + 87

and it will show the graph and various properties of the function. You will be able to see clearly that there is no horizontal tangent.