Find local extrema
Find critical points and classify local min/max for polynomials.
Also known as: find local extrema calculator, critical points calculator, find local extrema, calculus math, calculus find local extrema
Inputs
Results update when you click Find extrema.
Critical points
1
f(x) = x^6 −2.0000x^5; solve f′(x) = 6.0000x^5 −10.0000x^4 = 0
Critical points
| x | f(x) | Type |
|---|---|---|
| 1.6667 | -4.2867 | local min |
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What this result means
Find critical points and classify local min/max for polynomials. f′(x)=0 at critical points; f″>0 → local min, f″<0 → local max.
Assumptions
- Rule dependency: Universal formula.
Second derivative test
f′(x)=0 at critical points; f″>0 → local min, f″<0 → local max.
Example
f(x) = x³ − 2x has critical points at x = ±√(2/3).
Frequently asked questions
Boundary extrema?+
Scan endpoints separately if needed — this finds interior critical points.