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受欢迎的函数 >

extreme y=x^4-x^2

解答

极值点

y = x^{4} - x^{2}

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) = 4 x^{3} - 2 x

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

极小值 (- \frac{1}{2}, - \frac{1}{4})

将

x = 0

代入

x^{4} - x^{2} : 0

极大值 (0, 0)

将

x = \frac{1}{2}

代入

x^{4} - x^{2} : - \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)=xe-2x^2-2y^2

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

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

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

extreme f(t)=tu(t-2)

e x t re m e f (t) = t u (t - 2)

extreme f(x)=x^3-5x^2-8x

e x t re m e f (x) = x^{3} - 5 x^{2} - 8 x

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

e x t re m e f (x, y) = - 2 y - 3 x + 6