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?
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?
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
$\displaystyle x = \frac{-6 \pm \sqrt{6^2 - 12}}{6}$
$\displaystyle = \frac{-6\pm \sqrt{24}}{6}$
$\displaystyle = -0.1835\ or\ -1.8165$