Question

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

Answer 1

At x = 0, there is a inflection.

Explanation:

y = `x^3` - 12x

`dy/dx` = 3`x^2` - 12
`d^2/dx^2`=6x

Set `d^2/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