Home > Calculus > Determining Points of Inflection for a Function

How do you find the inflection points when given a graph?

Answer 1

Locate the points on the graph where the concavity changes. (This method is highly imprecise and ought to be saved for situations where the function has no formula.)

graph{[-1.709, 1.709, -0.855, 0.854]} x^3-x^2

Clearly there is an inflection point somewhere between #0# and #1/2#. I find it difficult to be more accurate than that.

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Answer 2

Aurora Alvarado

To find inflection points on a graph, you need to:

Determine the second derivative of the function.
Set the second derivative equal to zero and solve for x to find the potential inflection points.
Test the sign of the second derivative around each potential inflection point to confirm whether it changes sign. If it does, the point is an inflection point.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.