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受欢迎的函数 >

extreme f(x)=4x^3+33x^2-36x-530

解答

极值点

f (x) = 4 x^{3} + 33 x^{2} - 36 x - 530

解答

极大值 (- 6, 10), 极小值 (\frac{1}{2}, - \frac{2157}{4})

求解步骤

f^{'} (x) = 12 x^{2} + 66 x - 36

Find intervals:

递增

: - \infty < x < - 6,

递减

: - 6 < x < \frac{1}{2},

递增

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

将

x = - 6

代入

4 x^{3} + 33 x^{2} - 36 x - 530 : 10

极大值 (- 6, 10)

将

x = \frac{1}{2}

代入

4 x^{3} + 33 x^{2} - 36 x - 530 : - \frac{2157}{4}

极小值 (\frac{1}{2}, - \frac{2157}{4})

极大值 (- 6, 10), 极小值 (\frac{1}{2}, - \frac{2157}{4})

作图

流行的例子

extreme y=-2x^3+540x^2

e x t re m e y = - 2 x^{3} + 540 x^{2}

extreme f(x,y)=x^3+4y^2-3x+1

e x t re m e f (x, y) = x^{3} + 4 y^{2} - 3 x + 1

extreme R(x,y)=-x^2-y^2+x+2y-1

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

extreme f(x)=9x^3-7x^2+3x+10

e x t re m e f (x) = 9 x^{3} - 7 x^{2} + 3 x + 10

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

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