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受欢迎的函数 >

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

解答

极值点

f (x) = (x - 2) (x + 2) (x + 4)

解答

极大值 (- \frac{2 ( 2 + 7 )}{3}, \frac{272 + 112 7}{27} - 16), 极小值 (\frac{2 ( 7 - 2 )}{3}, \frac{272 - 112 7}{27} - 16)

求解步骤

f^{'} (x) = 3 x^{2} + 8 x - 4

Find intervals:

递增

: - \infty < x < \frac{- 2 7 - 4}{3},

递减

: \frac{- 2 7 - 4}{3} < x < \frac{2 7 - 4}{3},

递增

: \frac{2 7 - 4}{3} < x < \infty

将

x = - \frac{2 ( 2 + 7 )}{3}

代入

(x - 2) (x + 2) (x + 4) : \frac{272 + 112 7}{27} - 16

极大值 (- \frac{2 ( 2 + 7 )}{3}, \frac{272 + 112 7}{27} - 16)

将

x = \frac{2 ( 7 - 2 )}{3}

代入

(x - 2) (x + 2) (x + 4) : \frac{272 - 112 7}{27} - 16

极小值 (\frac{2 ( 7 - 2 )}{3}, \frac{272 - 112 7}{27} - 16)

极大值 (- \frac{2 ( 2 + 7 )}{3}, \frac{272 + 112 7}{27} - 16), 极小值 (\frac{2 ( 7 - 2 )}{3}, \frac{272 - 112 7}{27} - 16)

作图

流行的例子

extreme f(x)=11+5x+x^2

e x t re m e f (x) = 11 + 5 x + x^{2}

extreme f(x)=x^2log_{3}(x)

e x t re m e f (x) = x^{2} lo g_{3} (x)

extreme f(x)=(x^2-9x+50)/(x-7)

e x t re m e f (x) = \frac{x ^{2} - 9 x + 50}{x - 7}

extreme-4/(x-7)

e x t re m e - \frac{4}{x - 7}

extreme f(x,y)=-4x^2-2y^2-8x+12y+5

e x t re m e f (x, y) = - 4 x^{2} - 2 y^{2} - 8 x + 12 y + 5