# What is the x-coordinate of the point of inflection on the graph of y = (1/3)x^3 + 5x^2+ 24?

Apr 3, 2015

$- 5$

$y = \left(\frac{1}{3}\right) {x}^{3} + 5 {x}^{2} + 24$

$y ' = {x}^{2} + 10 x$

$y ' ' = 2 x + 10$, which is $0$ at $x = - 5$

The only place that the graph might change concavity is at the point where $x = - 5$

If you check, you'll find that $y ' '$ is negative for $x < - 5$ and positive for $x > - 5$. So the concavity changes at $\left(- 5 , \frac{322}{3}\right)$