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受欢迎的函数 >

extreme f(x)=x^6-x^4

解答

极值点

f (x) = x^{6} - x^{4}

解答

极小值 (- \frac{2}{3}, - \frac{4}{27}), 极大值 (0, 0), 极小值 (\frac{2}{3}, - \frac{4}{27})

求解步骤

f^{'} (x) = 6 x^{5} - 4 x^{3}

Find intervals:

递减

: - \infty < x < - \frac{2}{3},

递增

: - \frac{2}{3} < x < 0,

递减

: 0 < x < \frac{2}{3},

递增

: \frac{2}{3} < x < \infty

将

x = - \frac{2}{3}

代入

x^{6} - x^{4} : - \frac{4}{27}

极小值 (- \frac{2}{3}, - \frac{4}{27})

将

x = 0

代入

x^{6} - x^{4} : 0

极大值 (0, 0)

将

x = \frac{2}{3}

代入

x^{6} - x^{4} : - \frac{4}{27}

极小值 (\frac{2}{3}, - \frac{4}{27})

极小值 (- \frac{2}{3}, - \frac{4}{27}), 极大值 (0, 0), 极小值 (\frac{2}{3}, - \frac{4}{27})

作图

流行的例子

extreme f(x,y)=3x^{(4)}y^{(5)}+6x-7y

e x t re m e f (x, y) = 3 x^{(4)} y^{(5)} + 6 x - 7 y

extreme (4x)/(x^2+4)

e x t re m e \frac{4 x}{x ^{2} + 4}

extreme f(x)=-0.018x^3+0.215x^2+0.057x+1

e x t re m e f (x) = - 0.018 x^{3} + 0.215 x^{2} + 0.057 x + 1

extreme f(x)=2x^3+9x^2-60x+7,-5<= x<= 5

e x t re m e f (x) = 2 x^{3} + 9 x^{2} - 60 x + 7, - 5 \leq x \leq 5

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

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