Posted by **Amy** on Tuesday, February 26, 2013 at 10:12am.

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

- Calculus -
**Steve**, Tuesday, February 26, 2013 at 10:30am
this is the same as asking where F'(x) = 0

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

where would that be?

- Calculus -
**Amy**, Tuesday, February 26, 2013 at 11:21am
6x4=24

2x6=12+12=24

so...2?

- Calculus -
**Steve**, Tuesday, February 26, 2013 at 11:30am
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.

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