Maxima, minima and inflection
Maxima, minima and inflection is an interactive experiment in Derivatives & Tangents, a free simulation from StudyFi Lab that runs right in your browser.
Stationary points are where f′(x) = 0 and the tangent is horizontal. If f′ changes from + to −, f has a local maximum there; from − to +, a local minimum; if the sign stays the same, it is a stationary inflection point. Where f″ changes sign, the curve switches between concave up and concave down: an inflection point.
Try this: Classify each “?” on the curve from the signs of f′ below, then switch on the classification to check. Finally set the cubic to a = 1, b = 0, c = 0.
Frequently asked questions
What does the “Maxima, minima and inflection” experiment show?
Stationary points are where f′(x) = 0 and the tangent is horizontal. If f′ changes from + to −, f has a local maximum there; from − to +, a local minimum; if the sign stays the same, it is a stationary inflection point. Where f″ changes sign, the curve switches between concave up and concave down: an inflection point.
How do I try “Maxima, minima and inflection”?
Classify each “?” on the curve from the signs of f′ below, then switch on the classification to check. Finally set the cubic to a = 1, b = 0, c = 0.
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