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受欢迎的函数 >

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

解答

极值点

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

解答

极大值 (\frac{1 - 5}{2}, - \frac{3 ( 3 - 5 )}{2} + 1 + 5), 极小值 (\frac{1 + 5}{2}, - \frac{3 ( 3 + 5 )}{2} + 1 - 5)

求解步骤

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

Find intervals:

递增

: - \infty < x < \frac{- 5 + 1}{2},

递减

: \frac{- 5 + 1}{2} < x < \frac{5 + 1}{2},

递增

: \frac{5 + 1}{2} < x < \infty

将

x = \frac{1 - 5}{2}

代入

2 x^{3} - 3 x^{2} - 6 x : - \frac{3 ( 3 - 5 )}{2} + 1 + 5

极大值 (\frac{1 - 5}{2}, - \frac{3 ( 3 - 5 )}{2} + 1 + 5)

将

x = \frac{1 + 5}{2}

代入

2 x^{3} - 3 x^{2} - 6 x : - \frac{3 ( 3 + 5 )}{2} + 1 - 5

极小值 (\frac{1 + 5}{2}, - \frac{3 ( 3 + 5 )}{2} + 1 - 5)

极大值 (\frac{1 - 5}{2}, - \frac{3 ( 3 - 5 )}{2} + 1 + 5), 极小值 (\frac{1 + 5}{2}, - \frac{3 ( 3 + 5 )}{2} + 1 - 5)

作图

流行的例子

extreme f(x,y)=x^2-2*x+2*y^2-4*y

e x t re m e f (x, y) = x^{2} - 2 \cdot x + 2 \cdot y^{2} - 4 \cdot y

extreme f(x)=0.00397t^2-0.593t+33.718

e x t re m e f (x) = 0.00397 t^{2} - 0.593 t + 33.718

extreme f(x)=f(x)=ex-x,-4<= x<= 2

e x t re m e f (x) = f (x) = e x - x, - 4 \leq x \leq 2

extreme f(x)=4x^2-48x+190

e x t re m e f (x) = 4 x^{2} - 48 x + 190

extreme f(x,y)=e^{9x^2+6y^2+1}

e x t re m e f (x, y) = e^{9 x^{2} + 6 y^{2} + 1}