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受欢迎的函数 >

extreme f(x)=x(27-41+2x)(41/2-x)

解答

极值点

f (x) = x (27 - 41 + 2 x) (\frac{41}{2} - x)

解答

极小值 (\frac{55 - 1303}{6}, \frac{24310 - 1303 1303}{54}), 极大值 (\frac{55 + 1303}{6}, \frac{1303 1303 + 24310}{54})

求解步骤

f^{'} (x) = - 6 x^{2} + 110 x - 287

Find intervals:

递减

: - \infty < x < \frac{- 1303 + 55}{6},

递增

: \frac{- 1303 + 55}{6} < x < \frac{1303 + 55}{6},

递减

: \frac{1303 + 55}{6} < x < \infty

将

x = \frac{55 - 1303}{6}

代入

x (27 - 41 + 2 x) (\frac{41}{2} - x) : \frac{24310 - 1303 1303}{54}

极小值 (\frac{55 - 1303}{6}, \frac{24310 - 1303 1303}{54})

将

x = \frac{55 + 1303}{6}

代入

x (27 - 41 + 2 x) (\frac{41}{2} - x) : \frac{1303 1303 + 24310}{54}

极大值 (\frac{55 + 1303}{6}, \frac{1303 1303 + 24310}{54})

极小值 (\frac{55 - 1303}{6}, \frac{24310 - 1303 1303}{54}), 极大值 (\frac{55 + 1303}{6}, \frac{1303 1303 + 24310}{54})

作图

流行的例子

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

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

extreme f(x)=(x+1)^7-7x-3

e x t re m e f (x) = (x + 1)^{7} - 7 x - 3

extreme f(x)=-x^2+4xy-5y^2-6x+22y+9

e x t re m e f (x) = - x^{2} + 4 x y - 5 y^{2} - 6 x + 22 y + 9

extreme f(x)=3(4-2x)e^{-x}

e x t re m e f (x) = 3 (4 - 2 x) e^{- x}

extreme f(x,y)=x^4

e x t re m e f (x, y) = x^{4}