An inflection point is a point on a curve at which a change in the direction of curvature occurs.
For instance if the curve looked like a hill, the inflection point will be where it will start to look like U.
Formula to calculate inflection point.
- We find the inflection by finding the second derivative of the curve’s function.
The sign of the derivative tells us whether the curve is concave downward or concave upward.
Example:
Lets take a curve with the following function.
y = x³ − 6x² + 12x − 5
Lets begin by finding our first derivative.
y = x³ − 6x² + 12x − 5
y’ = 3x² – 12x
Then find our second derivative.
y’ = 3x² – 12x
y” = 6x -12
When we simplify our second derivative we get;
6x = 12
x = 2
This means that f(x) is concave downward up to x = 2 f(x) is concave upward from x = 2.
Therefore, our inflection point is at x = 2.
