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受欢迎的函数 >

extreme f(x)= 1/3 x^3-9x^2+72x+2

解答

极值点

f (x) = \frac{1}{3} x^{3} - 9 x^{2} + 72 x + 2

解答

极大值 (6, 182), 极小值 (12, 146)

求解步骤

f^{'} (x) = x^{2} - 18 x + 72

Find intervals:

递增

: - \infty < x < 6,

递减

: 6 < x < 12,

递增

: 12 < x < \infty

将

x = 6

代入

\frac{1}{3} x^{3} - 9 x^{2} + 72 x + 2 : 182

极大值 (6, 182)

将

x = 12

代入

\frac{1}{3} x^{3} - 9 x^{2} + 72 x + 2 : 146

极小值 (12, 146)

极大值 (6, 182), 极小值 (12, 146)

作图

流行的例子

extreme F(x,y)=x^3y^2+x^2y+2xy^2+2y

e x t re m e F (x, y) = x^{3} y^{2} + x^{2} y + 2 x y^{2} + 2 y

extreme f(x)= 1/x+x

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extreme f(x)=(x/5)^5-((4x)/4)^4+5

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extreme f(x)=x^4-2x^3-11x^2+12x+36

e x t re m e f (x) = x^{4} - 2 x^{3} - 11 x^{2} + 12 x + 36