Question

Where would `f(x)= -14x^3 + 19x^3 - x - 2` have an inflection point?

Answer 1

First of all I think there is a mistake in your writing, the second term I suppose it would be `19x^2`.

This is a cubic function that always has an only inflection point.
This is the only zero of the second derivative.

`y'=-42x^2+38x-1`

and

`y''=-84x+38` that is zero in `x=38/84=19/42`.