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受欢迎的函数 >

extreme f(x)=(x^2(x-3))/(x+6)

解答

极值点

f (x) = \frac{x ^{2} ( x - 3 )}{x + 6}

解答

极小值 (\frac{- 15 - 3 57}{4}, \frac{9 ( 19 57 + 143 )}{8}), 极大值 (0, 0), 极小值 (\frac{- 15 + 3 57}{4}, - \frac{9 ( 19 57 - 143 )}{8})

求解步骤

f^{'} (x) = \frac{2 x ^{3} + 15 x ^{2} - 36 x}{( x + 6 ) ^{2}}

Find intervals:

递减

: - \infty < x < \frac{- 15 - 3 57}{4},

递增

: \frac{- 15 - 3 57}{4} < x < - 6,

递增

: - 6 < x < 0,

递减

: 0 < x < \frac{3 57 - 15}{4},

递增

: \frac{3 57 - 15}{4} < x < \infty

将

x = \frac{- 15 - 3 57}{4}

代入

\frac{x ^{2} ( x - 3 )}{x + 6} : \frac{9 ( 19 57 + 143 )}{8}

极小值 (\frac{- 15 - 3 57}{4}, \frac{9 ( 19 57 + 143 )}{8})

将

x = 0

代入

\frac{x ^{2} ( x - 3 )}{x + 6} : 0

极大值 (0, 0)

将

x = \frac{- 15 + 3 57}{4}

代入

\frac{x ^{2} ( x - 3 )}{x + 6} : - \frac{9 ( 19 57 - 143 )}{8}

极小值 (\frac{- 15 + 3 57}{4}, - \frac{9 ( 19 57 - 143 )}{8})

极小值 (\frac{- 15 - 3 57}{4}, \frac{9 ( 19 57 + 143 )}{8}), 极大值 (0, 0), 极小值 (\frac{- 15 + 3 57}{4}, - \frac{9 ( 19 57 - 143 )}{8})

作图

流行的例子

extreme f(x)=f(x)=xsqrt(x^2+4)

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

extreme f(x)=2x^3+3x^2-120x+9

e x t re m e f (x) = 2 x^{3} + 3 x^{2} - 120 x + 9

extreme f(x)=x^3+12x^2-27x+6,-10<= x<= 0

e x t re m e f (x) = x^{3} + 12 x^{2} - 27 x + 6, - 10 \leq x \leq 0

extreme y=(2x^2-1)^2

e x t re m e y = (2 x^{2} - 1)^{2}

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

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