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^2-6x+12
where would that be?
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.