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受欢迎的函数 >

extreme f(x)=x-1/6 x^2-2/3 ln(x)

解答

极值点

f (x) = x - \frac{1}{6} x^{2} - \frac{2}{3} ln (x)

解答

极小值 (1, \frac{5}{6}), 极大值 (2, \frac{4}{3} - \frac{2}{3} ln (2))

求解步骤

f^{'} (x) = 1 - \frac{x}{3} - \frac{2}{3 x}

Find intervals:

递减

: 0 < x < 1,

递增

: 1 < x < 2,

递减

: 2 < x < \infty

将

x = 1

代入

x - \frac{1}{6} x^{2} - \frac{2}{3} ln (x) : \frac{5}{6}

极小值 (1, \frac{5}{6})

将

x = 2

代入

x - \frac{1}{6} x^{2} - \frac{2}{3} ln (x) : \frac{4}{3} - \frac{2}{3} ln (2)

极大值 (2, \frac{4}{3} - \frac{2}{3} ln (2))

极小值 (1, \frac{5}{6}), 极大值 (2, \frac{4}{3} - \frac{2}{3} ln (2))

作图

流行的例子

extreme y=x^3-6x^2+9x-8

e x t re m e y = x^{3} - 6 x^{2} + 9 x - 8

extreme f(x)=12+2x-x^2

e x t re m e f (x) = 12 + 2 x - x^{2}

extreme f(x)=(x^2-24)/(x-5)

e x t re m e f (x) = \frac{x ^{2} - 24}{x - 5}

extreme f(x)=ln(x)-x

e x t re m e f (x) = ln (x) - x

extreme f(x)=(4x)/(x^2+25)

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