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受欢迎的函数 >

extreme f(x)=x^2(x^2-1)

解答

极值点

f (x) = x^{2} (x^{2} - 1)

解答

极小值 (- \frac{1}{2}, - \frac{1}{4}), 极大值 (0, 0), 极小值 (\frac{1}{2}, - \frac{1}{4})

求解步骤

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

Find intervals:

递减

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

递增

: - \frac{1}{2} < x < 0,

递减

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

递增

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

将

x = - \frac{1}{2}

代入

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

极小值 (- \frac{1}{2}, - \frac{1}{4})

将

x = 0

代入

x^{2} (x^{2} - 1) : 0

极大值 (0, 0)

将

x = \frac{1}{2}

代入

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

极小值 (\frac{1}{2}, - \frac{1}{4})

极小值 (- \frac{1}{2}, - \frac{1}{4}), 极大值 (0, 0), 极小值 (\frac{1}{2}, - \frac{1}{4})

作图

流行的例子

extreme f(x,y)=x^2+2y^2+xy-5x-6y

e x t re m e f (x, y) = x^{2} + 2 y^{2} + x y - 5 x - 6 y

extreme f(x)=(x^2-5)/(x+3)

e x t re m e f (x) = \frac{x ^{2} - 5}{x + 3}

extreme f(x)= x/(sqrt(x-4)),6<= x<= 10

e x t re m e f (x) = \frac{x}{x - 4}, 6 \leq x \leq 10

extreme f(x)=(x-1)^2+(y-2)^2

e x t re m e f (x) = (x - 1)^{2} + (y - 2)^{2}

extreme f(x)=(3x^2)/(x^2-16)

e x t re m e f (x) = \frac{3 x ^{2}}{x ^{2} - 16}