Local Maxima And Minima Calculator
Work out local maxima and minima instantly with clear inputs, formula shown and shareable results.
About Local Maxima And Minima Calculator
Local extrema occur at critical points where the derivative changes sign. A negative second derivative means the curve bends downward, giving a local maximum; a positive one gives a local minimum.
Formula
Second derivative test
f'(c) = 0 and f''(c) < 0 ⇒ local maximum; f''(c) > 0 ⇒ local minimum
Worked example
With the default values below, Local Maxima And Minima Calculator returns Local maxima of x = -2, f = 16. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Polynomial coefficients, highest power first
- 1, 0, -12, 0
- Search from x =
- -5
- Search to x =
- 5
Results
- Local maxima
- x = -2, f = 16
- Local minima
- x = 2, f = -16
- Number of maxima
- 1
- Number of minima
- 1
Step by step
- 1Values used
- 2Second derivative test
- 3Local maxima= x = -2, f = 16
- 4Local minima= x = 2, f = -16
- 5Number of maxima= 1
- 6Number of minima= 1
Assumptions and limits
- The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to whole numbers, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
For x³ − 12x?
f' = 3x² − 12 gives x = ±2, with a maximum at x = −2 (f = 16) and a minimum at x = 2 (f = −16).
Are local extrema always global?
No. A cubic has local extrema but is unbounded, so neither is a global maximum or minimum.