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**.