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受欢迎的函数 >

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

解答

极值点

f (x) = 2 x^{3} + 3 x^{2} - 2 x - 2

解答

极大值 (- \frac{3 + 21}{6}, \frac{27 + 7 21}{18} - 2), 极小值 (\frac{- 3 + 21}{6}, \frac{27 - 7 21}{18} - 2)

求解步骤

f^{'} (x) = 6 x^{2} + 6 x - 2

Find intervals:

递增

: - \infty < x < - \frac{7}{2 3} - \frac{1}{2},

递减

: - \frac{7}{2 3} - \frac{1}{2} < x < \frac{7}{2 3} - \frac{1}{2},

递增

: \frac{7}{2 3} - \frac{1}{2} < x < \infty

将

x = - \frac{3 + 21}{6}

代入

2 x^{3} + 3 x^{2} - 2 x - 2 : \frac{27 + 7 21}{18} - 2

极大值 (- \frac{3 + 21}{6}, \frac{27 + 7 21}{18} - 2)

将

x = \frac{- 3 + 21}{6}

代入

2 x^{3} + 3 x^{2} - 2 x - 2 : \frac{27 - 7 21}{18} - 2

极小值 (\frac{- 3 + 21}{6}, \frac{27 - 7 21}{18} - 2)

极大值 (- \frac{3 + 21}{6}, \frac{27 + 7 21}{18} - 2), 极小值 (\frac{- 3 + 21}{6}, \frac{27 - 7 21}{18} - 2)

作图

流行的例子

extreme f(x,y)=60x+34y-4xy-6x^2-3y^2+5

e x t re m e f (x, y) = 60 x + 34 y - 4 x y - 6 x^{2} - 3 y^{2} + 5

extreme f(x)=x^2*e^{-x^2}

e x t re m e f (x) = x^{2} \cdot e^{- x^{2}}

extreme f(x)=x^3-12x^2+45x+2

e x t re m e f (x) = x^{3} - 12 x^{2} + 45 x + 2

extreme f(x)=-5x^3-4x^4

e x t re m e f (x) = - 5 x^{3} - 4 x^{4}

extreme f(x)=x^2+3y^2-2x+18y

e x t re m e f (x) = x^{2} + 3 y^{2} - 2 x + 18 y