Extremum Command
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This command differs among variants of English:
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- Extremum( <Polynomial> )
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Yields all local extrema of the polynomial function as points on the function graph.
Extremum(x³ + 3x² - 2x + 1) creates local extrema (0.29, 0.70) and (-2.29, 9.30) and shows them in the
Graphics
View.
- Extremum( <Function>, <Start x-Value>, <End x-Value> )
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Calculates (numerically) the extremum of the function in the open interval ( <Start x-Value>, <End x-Value> ).
Extremum((x⁴ - 3x³ - 4x² + 4) / 2, 0, 5) creates local extremum (2.93, -16.05) in the given interval and shows
it in the
Graphics View.
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The function should be continuous in [ <Start x-Value>, <End x-Value> ], otherwise false extrema near discontinuity might be calculated. |
CAS Syntax
- Extremum( <Function> )
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Will attempt to return all local extrema of the function (which should be continuous and differentiable)
Extremum(x³ + 3x² - 2x + 1) creates a list of the points and plots them \( \left\\{ \left(\frac{-\sqrt{15}
- 3}\{3}, \frac{10 \; \sqrt{15} + 45}\{9} \right), \left(\frac{\sqrt{15} - 3}\{3}, \frac{-10 \; \sqrt{15} +
45}\{9} \right) \right\}\).
Assume(0 < x < 20, Extremum(15/2 * sin( 2/15*pi * x) + 56/5)) yields the local turning points in the range given
\( \left\\{ \left(\frac{15}\{4}, \frac{187}\{10} \right), \left(\frac{45}\{4}, \frac{37}\{10} \right),
\left(\frac{75}\{4}, \frac{187}\{10} \right) \right\} \).