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受欢迎的函数 >

extreme f(x)=-x^3-x^2+5x-4

解答

极值点

f (x) = - x^{3} - x^{2} + 5 x - 4

解答

极小值 (- \frac{5}{3}, - \frac{283}{27}), 极大值 (1, - 1)

求解步骤

f^{'} (x) = - 3 x^{2} - 2 x + 5

Find intervals:

递减

: - \infty < x < - \frac{5}{3},

递增

: - \frac{5}{3} < x < 1,

递减

: 1 < x < \infty

将

x = - \frac{5}{3}

代入

- x^{3} - x^{2} + 5 x - 4 : - \frac{283}{27}

极小值 (- \frac{5}{3}, - \frac{283}{27})

将

x = 1

代入

- x^{3} - x^{2} + 5 x - 4 : - 1

极大值 (1, - 1)

极小值 (- \frac{5}{3}, - \frac{283}{27}), 极大值 (1, - 1)

作图

流行的例子

extreme f(x)=-x^3-x^2+5x-5

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

extreme f(x)=-x^3-x^2+5x-3

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

extreme f(x)=4x^3-440x^2+10500x

e x t re m e f (x) = 4 x^{3} - 440 x^{2} + 10500 x

extreme f(x)=4+15x+6x^2-x^3

e x t re m e f (x) = 4 + 15 x + 6 x^{2} - x^{3}

extreme g(x,y)=4x+9y

e x t re m e g (x, y) = 4 x + 9 y