臨界点と極値の計算機
臨界点と極値をステップバイステップで求める
この計算機は、一変数関数の臨界点(停留点)、相対(局所)および絶対(大域)の最大値と最小値を求めます。区間を指定できます。
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.