Inflection Point Calculator
Supported formats: x^3, sin(x), cos(x), etc.
Results
What is an Inflection Point?
An inflection point is a point on a continuous plane curve where the curve changes from being concave upwards to concave downwards, or vice versa. In calculus terms, it’s a point where the second derivative of a function changes sign. At an inflection point, the tangent line crosses the curve, indicating a change in the curve’s concavity.
How to Find Function Inflection Points
Step 1
Enter your mathematical function in the input field using standard mathematical notation. For example, type “x^3 – 3x” for a cubic function.
Step 2
Ensure your function is written correctly using supported mathematical operators: ^ for exponents, * for multiplication, / for division, and standard notation for trigonometric functions.
Step 3
Click the calculate button and observe the results. The calculator will display both the coordinates of the inflection point(s) and a detailed explanation of the calculation process.
Step 4
Review the provided explanation to understand how the inflection points were determined through derivatives and critical points analysis.
Step 5
For complex functions, verify the results by checking if the second derivative changes sign at the calculated points and if the concavity of the function changes.