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受欢迎的函数 >

extreme 4x^2-8x^4

解答

极值点

4 x^{2} - 8 x^{4}

解答

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

求解步骤

f^{'} (x) = 8 x - 32 x^{3}

Find intervals:

递增

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

递减

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

递增

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

递减

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

将

x = - \frac{1}{2}

代入

4 x^{2} - 8 x^{4} : \frac{1}{2}

极大值 (- \frac{1}{2}, \frac{1}{2})

将

x = 0

代入

4 x^{2} - 8 x^{4} : 0

极小值 (0, 0)

将

x = \frac{1}{2}

代入

4 x^{2} - 8 x^{4} : \frac{1}{2}

极大值 (\frac{1}{2}, \frac{1}{2})

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

作图

流行的例子

extreme f(x)=(x^2(x-1))/(x+2),x\ne 2

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

extreme f(x)=9x^3+21x^2+8x-3

e x t re m e f (x) = 9 x^{3} + 21 x^{2} + 8 x - 3

extreme f(x)=x^2-2x+5[-1.4]

e x t re m e f (x) = x^{2} - 2 x + 5 [- 1.4]

extreme 2x^4-196x^2-3

e x t re m e 2 x^{4} - 196 x^{2} - 3

extreme f(x)=-x^2-y^2+8x+8y

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