Points of inflection from the graphs of f, f' or f'' | Summary and Q&A

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June 29, 2018
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blackpenredpen
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Points of inflection from the graphs of f, f' or f''

TL;DR

The video explains how to find inflection points in a function using the original function, its first derivative, and its second derivative.

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Questions & Answers

Q: How do you find inflection points in the original function?

Look for the points where the concavity changes from concave up to down or from concave down to up. These changes indicate inflection points.

Q: What approach should be used when given only the first derivative?

In this case, the second derivative can be interpreted as the slope of the tangent line of the first derivative. Identify where the slope changes signs to locate the inflection points.

Q: How do you find inflection points if the second derivative is given?

Look for where the second derivative changes signs. Positive values indicate regions above the x-axis, while negative values represent regions below the x-axis. The points where the sign changes are the inflection points.

Q: What are the inflection points for the first derivative graph provided in the video?

The inflection points for the first derivative graph are at x = 2, x = 4, and x = 6.

Summary & Key Takeaways

  • To find inflection points in the original function, look for where the concavity changes from up to down or vice versa.

  • When given only the first derivative, find where the slope changes sign to locate the inflection points.

  • If provided with the second derivative, identify where the value changes signs to determine the points of inflection.

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