# What are the coordinates of the point of inflection on the graph of y=x^3-15x^2+33x+100?

Nov 11, 2016

(5,15)

#### Explanation:

To find the inflection point, you will need to take the second derivative.

$y = {x}^{3} - 15 {x}^{2} + 33 x + 100$

$y ' = 3 {x}^{2} - 30 x + 33$

$y ' ' = 6 x - 30$

$6 x = 30$

$x = 5$

Now that you have your $x$, plug it into your first equation:

$y \left(5\right) = {\left(5\right)}^{3} - 15 {\left(5\right)}^{2} + 33 \left(5\right) + 100$
$= 125 - 375 + 165 + 100 = 15$
The inflection point is (5,15)