# How do you find the inflection points of the graph of the function:  f(x)= x^3 - 12x?

Aug 19, 2015

At x = 0, there is a inflection.

#### Explanation:

y = ${x}^{3}$ - 12x

$\frac{\mathrm{dy}}{\mathrm{dx}}$ = 3${x}^{2}$ - 12
${d}^{2} / {\mathrm{dx}}^{2}$=6x

Set ${d}^{2} / {\mathrm{dx}}^{2}$=0 => 6x = 0
Take a few values on either side. The co-ordinates -

x y
-3 9
-2 16
-1 11
0 0
1 -11
2 -16
3 -9
The graph