Question

How do you find the inflection point of a cubic function?

Answer 1

If `y=f(x)` is the cubic, and if you know how to take the derivative `f'(x)`, do it again to get `f''(x)` and solve `f''(x) = 0` for `x`; the inflection point of the curve is at `(x, f(x))`.

The 2nd derivative measures the concavity, down or up, and the inflection point is where that changes from negative to positive, so `f"` is equal to 0 there.

If you don't know calculus, then try to find the center of symmetry; any line that meets the cubic curve in 3 equally spaced points has the inflection point as the middle.

Hope this helps; @dansmath to the rescue!