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Inflection Point Calculation Formula
The following formula is used to calculate the inflection point of a function:
Inflection Point: f''(x) = 0
Variables:
- Inflection Point is the point on the curve where the concavity changes.
- f”(x) is the second derivative of the function.
To find the inflection point, solve for x where the second derivative equals zero and ensure the concavity changes at that point.
What is an Inflection Point?
An inflection point is a point on a curve where the sign of the curvature (concavity) changes. In other words, it is where the curve changes from being concave upwards (cup-shaped) to concave downwards (cap-shaped), or vice versa. Finding the inflection point is important in calculus as it helps in understanding the behavior of the function and its graph.
How to Calculate an Inflection Point?
The following steps outline how to calculate an inflection point using the given formula.
- First, determine the first and second derivatives of the function.
- Next, set the second derivative equal to zero and solve for x.
- Verify that the concavity changes at the