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受欢迎的函数 >

extreme f(x)= 1/2 ln((1+x)/(1-x))-2x

解答

极值点

f (x) = \frac{1}{2} ln (\frac{1 + x}{1 - x}) - 2 x

解答

极大值 (- \frac{1}{2}, \frac{1}{2} ln (3 - 22) + 2), 极小值 (\frac{1}{2}, \frac{1}{2} ln (3 + 22) - 2)

求解步骤

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

Find intervals:

递增

: - 1 < x < - \frac{1}{2},

递减

: - \frac{1}{2} < x < \frac{1}{2},

递增

: \frac{1}{2} < x < 1

将

x = - \frac{1}{2}

代入

\frac{1}{2} ln (\frac{1 + x}{1 - x}) - 2 x : \frac{1}{2} ln (3 - 22) + 2

极大值 (- \frac{1}{2}, \frac{1}{2} ln (3 - 22) + 2)

将

x = \frac{1}{2}

代入

\frac{1}{2} ln (\frac{1 + x}{1 - x}) - 2 x : \frac{1}{2} ln (3 + 22) - 2

极小值 (\frac{1}{2}, \frac{1}{2} ln (3 + 22) - 2)

极大值 (- \frac{1}{2}, \frac{1}{2} ln (3 - 22) + 2), 极小值 (\frac{1}{2}, \frac{1}{2} ln (3 + 22) - 2)

作图

流行的例子

extreme f(x)=6x+12y-x^2-3y^2

e x t re m e f (x) = 6 x + 12 y - x^{2} - 3 y^{2}

extreme f(x)=x^{2/5}(x-8)

e x t re m e f (x) = x^{\frac{2}{5}} (x - 8)

extreme f(x)=(x/2)+1/x

e x t re m e f (x) = (\frac{x}{2}) + \frac{1}{x}

extreme f(x)=x^2+8x+16

e x t re m e f (x) = x^{2} + 8 x + 16

extreme f(x,y)=xy+4/x+2/y

e x t re m e f (x, y) = x y + \frac{4}{x} + \frac{2}{y}