Classify stationary points by derivative sign changes. Each submitted value produces local extrema plus the intermediate reasoning.
Rework Local Extrema without copying Local extrema. Begin with Function f(x) and preserve Interval start. Predict the scale of the Local Extrema answer, then compare it with Local extrema. Store a changed Interval end as another Local Extrema case.
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.
Find numerical derivative zeros and test the derivative immediately to each side.
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.
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.
Inspect the domain of Function f(x) before using Local Extrema. Keep exact Local Extrema work separate from Interval start.
Test Local Extrema on a constant or linear function. Refine any numerical Local Extrema step and compare the approximation.
Preserve the first Local Extrema case before testing another value of Function f(x). Leave Interval start unchanged so a shift in Local extrema has one cause. Recording both values of Local extrema also prevents the revised Local Extrema data from replacing the original silently.
Yes.
Not as interior local extrema here.
By derivative sign change.