Calculus
posted by Amy .
For what values of x does the graph of F9x) = 2x^3  3x^2 + 12x + 87 have a horizontal tangent?

this is the same as asking where F'(x) = 0
Since F'(x) = 6x^26x+12
where would that be? 
6x4=24
2x6=12+12=24
so...2? 
No, it's almost a trick question.
6x^26x+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.