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^26x+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^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.
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