|
|
|
|
|
|
|
|
|
|
|
|
臨界點與極值計算器
逐步求臨界點與極值
此計算器將嘗試尋找單變數函數的臨界（駐）點，以及相對（局部）與絕對（全域）的極大值和極小值。可指定區間。
Your input: find the local and global minima and maxima of $$$f=x^{4} - 6 x^{2}$$$
Critical Points
$$$\left(x, f \left(x \right)\right)=\left(- \sqrt{3},-9\right)\approx \left(-1.73205080756888,-9\right)$$$
$$$\left(x, f \left(x \right)\right)=\left(0,0\right)$$$
$$$\left(x, f \left(x \right)\right)=\left(\sqrt{3},-9\right)\approx \left(1.73205080756888,-9\right)$$$
Global (Absolute) Minima
$$$\left(x, f \left(x \right)\right)=\left(- \sqrt{3},-9\right)\approx \left(-1.73205080756888,-9\right)$$$
$$$\left(x, f \left(x \right)\right)=\left(\sqrt{3},-9\right)\approx \left(1.73205080756888,-9\right)$$$
Global (Absolute) Maxima
No global maxima.
Local Minima
$$$\left(x, f \left(x \right)\right)=\left(- \sqrt{3},-9\right)\approx \left(-1.73205080756888,-9\right)$$$
$$$\left(x, f \left(x \right)\right)=\left(\sqrt{3},-9\right)\approx \left(1.73205080756888,-9\right)$$$
Local Maxima
$$$\left(x, f \left(x \right)\right)=\left(0,0\right)$$$
Graph
For graph, see graphing calculator.