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?

Printable View

- Sep 26th 2009, 07:58 PMjayjay60horizontal tangent
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? - Sep 26th 2009, 08:01 PMdifferentiate
yes, Differentiate first.

- Sep 26th 2009, 08:10 PMjayjay60
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. >.<,

- Sep 26th 2009, 08:49 PMdifferentiate
Yep set it to zero.

it becomes

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

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

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

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

the answer becomes

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

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

$\displaystyle = -0.1835\ or\ -1.8165$