horizontal tangent

**jayjay60** · September 26th 2009, 07:58 PM

For what values of x does the graph of f (x) have a horizontal tangent? (Round the answers to three decimal places.)
f (x) = 2x^3 + 6x^2 + 2 x + 9

horizontal tangent has a zero slope
so would i differentiate it before i set the equation =0?

**differentiate** · September 26th 2009, 08:01 PM

yes, Differentiate first.

**jayjay60** · September 26th 2009, 08:10 PM

well i got 6x^2+12x+2, do i set this equal to 0 or what next? i've been studying math all day long. i'm f'serious. >.<,

**differentiate** · September 26th 2009, 08:49 PM

Yep set it to zero.
it becomes

$6x^2 + 12x + 2 = 0$

$2(3x^2 + 6x + 1) = 0$

$3x^2 + 6x + 1 = 0$

and then find the values of x, using the quadratic formula or completing the square.

the answer becomes

$x = \frac{-6 \pm \sqrt{6^2 - 12}}{6}$

$= \frac{-6\pm \sqrt{24}}{6}$

$= -0.1835\ or\ -1.8165$

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