# What are the points of inflection, if any, of f(x)=-3x^3+270x^2-3600x+18000 ?

Oct 28, 2016

At $x = 30$, there is a point of inflection

#### Explanation:

Given -

$y = - 3 {x}^{3} + 270 {x}^{2} - 3600 x + 18000$

To find the point of inflection we have to set the send derivative equal to zero.

$\frac{\mathrm{dy}}{\mathrm{dx}} = 9 {x}^{2} + 540 x - 3600$

$\frac{{d}^{2} y}{{\mathrm{dx}}^{2}} = 18 x + 540$

Set $\frac{{d}^{2} y}{{\mathrm{dx}}^{2}} = 0$

Then -

$18 x + 540 = 0$
$x = \frac{540}{18} = 30$

At $x = 30$, there is a point of inflection