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受欢迎的函数 >

extreme f(x)=x(25-46+2x)(46/2-x)

解答

极值点

f (x) = x (25 - 46 + 2 x) (\frac{46}{2} - x)

解答

极小值 (\frac{67 - 1591}{6}, \frac{9514 - 1591 1591}{54}), 极大值 (\frac{67 + 1591}{6}, \frac{1591 1591 + 9514}{54})

求解步骤

f^{'} (x) = - 6 x^{2} + 134 x - 483

Find intervals:

递减

: - \infty < x < \frac{- 1591 + 67}{6},

递增

: \frac{- 1591 + 67}{6} < x < \frac{1591 + 67}{6},

递减

: \frac{1591 + 67}{6} < x < \infty

将

x = \frac{67 - 1591}{6}

代入

x (25 - 46 + 2 x) (\frac{46}{2} - x) : \frac{9514 - 1591 1591}{54}

极小值 (\frac{67 - 1591}{6}, \frac{9514 - 1591 1591}{54})

将

x = \frac{67 + 1591}{6}

代入

x (25 - 46 + 2 x) (\frac{46}{2} - x) : \frac{1591 1591 + 9514}{54}

极大值 (\frac{67 + 1591}{6}, \frac{1591 1591 + 9514}{54})

极小值 (\frac{67 - 1591}{6}, \frac{9514 - 1591 1591}{54}), 极大值 (\frac{67 + 1591}{6}, \frac{1591 1591 + 9514}{54})

作图

流行的例子

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

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

extreme y=x^5-15x^3+100

e x t re m e y = x^{5} - 15 x^{3} + 100

extreme f(x)=(ln(x^2+1))

e x t re m e f (x) = (ln (x^{2} + 1))

extreme f(x)=3x+5x^{-1}

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

extreme f(x)=(x-1)^5

e x t re m e f (x) = (x - 1)^{5}