Classify stationary points by derivative sign changes. Each submitted value produces local extrema plus the intermediate reasoning.
Local extrema locate peaks, valleys, operating optima, and graph landmarks. A related application of Local Extrema is candidate points.
A derivative change from positive to negative marks a local maximum; negative to positive marks a local minimum. Local Extrema can be checked against sign intervals.
This definition sets the boundary between local extrema and a neighboring calculation with similar inputs.
For x³−3x, x=−1 is a local maximum and x=1 a local minimum.
Stationary points without a sign change are not extrema, and interval endpoints need a separate endpoint comparison.
An impossible local extrema sign or magnitude usually points to field assignment before it points to rounding.
Find numerical derivative zeros and test the derivative immediately to each side.
Start the local extrema setup by pairing every source number with Function f(x), Interval start and Interval end. Convert unlike units before typing, and postpone rounding until the displayed local extrema is ready to report.
Changing the interval can add or remove reported candidates but does not alter their local classification. Use that direction of change to check the displayed local extrema before copying it elsewhere.
Critical-point search lists candidates without deciding maximum or minimum. Keep that boundary in mind when interpreting the numerical result.
When copying the result elsewhere, include its label and any squared, linear, angular, or percentage unit implied by the inputs. That record distinguishes a calculated local extrema from an unlabeled number and makes later checking substantially easier.
For later verification, record Function f(x), Interval start and Interval end before rounding the local extrema. The unrounded working value can feed subsequent steps while the rounded value serves presentation.
The entries defining Local Extrema are Function f(x), Interval start, and Interval end. Vary one numerical setting while leaving the mathematical problem unchanged. A defensible result should settle as resolution improves. Treat agreement after rounding alone cautiously when the unrounded estimates continue to move.
For this local extrema result, a useful record includes the function, relevant bounds, and the numerical convention used here. Those details matter more than the calculator interface and prevent an approximation from being quoted as a symbolic identity.
Yes.
Not as interior local extrema here.
By derivative sign change.