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受欢迎的函数 >

extreme f(x)=x^3+4x^2-3x+6

解答

极值点

f (x) = x^{3} + 4 x^{2} - 3 x + 6

解答

极大值 (- 3, 24), 极小值 (\frac{1}{3}, \frac{148}{27})

求解步骤

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

Find intervals:

递增

: - \infty < x < - 3,

递减

: - 3 < x < \frac{1}{3},

递增

: \frac{1}{3} < x < \infty

将

x = - 3

代入

x^{3} + 4 x^{2} - 3 x + 6 : 24

极大值 (- 3, 24)

将

x = \frac{1}{3}

代入

x^{3} + 4 x^{2} - 3 x + 6 : \frac{148}{27}

极小值 (\frac{1}{3}, \frac{148}{27})

极大值 (- 3, 24), 极小值 (\frac{1}{3}, \frac{148}{27})

作图

流行的例子

extreme f(x,y)=x^3+y^3+2x^2+4y^2+6

e x t re m e f (x, y) = x^{3} + y^{3} + 2 x^{2} + 4 y^{2} + 6

extreme f(x,y)=5+3x^2+3y^2+2y^3+x^3

e x t re m e f (x, y) = 5 + 3 x^{2} + 3 y^{2} + 2 y^{3} + x^{3}

extreme f(x)=4+x^3+y^3-3xy

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

extreme x^{2/3}-6x^{-1/3}

e x t re m e x^{\frac{2}{3}} - 6 x^{- \frac{1}{3}}

extreme f(x,y)=2x+y+2/x-(y^2)/2

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