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受欢迎的函数 >

extreme f(x)=x^{2/3 (x-3)}

解答

极值点

f (x) = x^{\frac{2}{3} (x - 3)}

解答

极小值 (\frac{3}{W _{0} ( 3 e )}, (\frac{3}{W _{0} ( 3 e )})^{\frac{2}{W _{0} ( 3 e )} - 2})

求解步骤

找到临界点:

x = \frac{3}{W _{0} ( 3 e )}

x^{\frac{2}{3} (x - 3)}

的定义域

: x > 0

Find intervals:

递减

: 0 < x < \frac{3}{W _{0} ( 3 e )},

递增

: \frac{3}{W _{0} ( 3 e )} < x < \infty

将极值点

x = \frac{3}{W _{0} ( 3 e )}

代入

x^{\frac{2}{3} (x - 3)} \Rightarrow y = (\frac{3}{W _{0} ( 3 e )})^{\frac{2}{W _{0} ( 3 e )} - 2}

极小值 (\frac{3}{W _{0} ( 3 e )}, (\frac{3}{W _{0} ( 3 e )})^{\frac{2}{W _{0} ( 3 e )} - 2})

作图

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