Question

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

Answer 1

`-5`

`y = (1/3)x^3 + 5x^2+ 24`

`y' = x^2 + 10x`

`y'' = 2x + 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 `(-5, 322/3)`