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受欢迎的函数 >

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

解答

极值点

f (x) = 3 x^{3} - 3 x

解答

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

求解步骤

f^{'} (x) = 9 x^{2} - 3

Find intervals:

递增

: - \infty < x < - \frac{1}{3},

递减

: - \frac{1}{3} < x < \frac{1}{3},

递增

: \frac{1}{3} < x < \infty

将

x = - \frac{1}{3}

代入

3 x^{3} - 3 x : - \frac{1}{3} + 3

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

将

x = \frac{1}{3}

代入

3 x^{3} - 3 x : \frac{1}{3} - 3

极小值 (\frac{1}{3}, \frac{1}{3} - 3)

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

作图

流行的例子

extreme f(x)=5x+10sin(x)

e x t re m e f (x) = 5 x + 10 sin (x)

extreme f(x,y)=-8x^3y+2xy^2-5x^2y^5+12x

e x t re m e f (x, y) = - 8 x^{3} y + 2 x y^{2} - 5 x^{2} y^{5} + 12 x

extreme f(x)=9x^4-4x^3

e x t re m e f (x) = 9 x^{4} - 4 x^{3}

extreme f(x)=(x^5-5x)/5

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

extreme f(x)=(x-3)(x+1)(x+5)

e x t re m e f (x) = (x - 3) (x + 1) (x + 5)