The point of inflection is the point on a curve where the concavity changes, such that the curve transitions from concave down to concave up or vice versa. Mathematically, it is the point where the second derivative equals zero or changes sign, indicating a switch between increasing and decreasing slope. To find the point of inflection, take the second derivative of a function and set it equal to zero to solve for the x-value where the concavity changes.

1. POINT OF INFLECTION

2. WHAT IS THE POINT OF INFLECTION
• An inflection point is the point where the concavity changes. At the inflection
point, the curve might go from concave down (with a decreasing slope) to concave
up(with an increasing slope). ... At the inflection point, the second
derivative changes from negative to positive, and must be zero.

3. GRAPH

5. • We decide the concavity from the 2nd derivative
Mathematically
IF the 2nd derivative = 0 at that point ( point of inflection )
OR
IF the 2nd derivative changes its sign at that point so (2nd derivative = 0)

6. • f(x) = 𝑥3
• First derivative f’(x) = 3𝑥2
• 2nd derivative f’’(x) = 6x
• Now set the second derivative equal to zero and solve for "x" to find possible
inflection points.

7. 2nd derivative = 0 6x = 0
x = 0