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受欢迎的函数 >

extreme x^3+8x^2-6x-4

解答

极值点

x^{3} + 8 x^{2} - 6 x - 4

解答

极大值 (- \frac{8 + 82}{3}, \frac{1024 + 110 82}{27} + 12 + 282), 极小值 (\frac{- 8 + 82}{3}, \frac{1024 - 110 82}{27} + 12 - 282)

求解步骤

f^{'} (x) = 3 x^{2} + 16 x - 6

Find intervals:

递增

: - \infty < x < \frac{- 82 - 8}{3},

递减

: \frac{- 82 - 8}{3} < x < \frac{82 - 8}{3},

递增

: \frac{82 - 8}{3} < x < \infty

将

x = - \frac{8 + 82}{3}

代入

x^{3} + 8 x^{2} - 6 x - 4 : \frac{1024 + 110 82}{27} + 12 + 282

极大值 (- \frac{8 + 82}{3}, \frac{1024 + 110 82}{27} + 12 + 282)

将

x = \frac{- 8 + 82}{3}

代入

x^{3} + 8 x^{2} - 6 x - 4 : \frac{1024 - 110 82}{27} + 12 - 282

极小值 (\frac{- 8 + 82}{3}, \frac{1024 - 110 82}{27} + 12 - 282)

极大值 (- \frac{8 + 82}{3}, \frac{1024 + 110 82}{27} + 12 + 282), 极小值 (\frac{- 8 + 82}{3}, \frac{1024 - 110 82}{27} + 12 - 282)

作图

流行的例子

extreme f(x)=-13/9 x^2+8/3 x^2+37/10

e x t re m e f (x) = - \frac{13}{9} x^{2} + \frac{8}{3} x^{2} + \frac{37}{10}

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

e x t re m e \frac{( x - 4 )}{x ^{2}}

extreme f(x)=(2x-6)/(sqrt(x^2+7)-4)

e x t re m e f (x) = \frac{2 x - 6}{x ^{2} + 7 - 4}

extreme f(x)=(5+x)+(1000+100x)

e x t re m e f (x) = (5 + x) + (1000 + 100 x)

extreme f(x)=-(x/3)^3+2x^2+12x+1

e x t re m e f (x) = - (\frac{x}{3})^{3} + 2 x^{2} + 12 x + 1