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受欢迎的函数 >

extreme 5x^2(x-11)+3

解答

极值点

5 x^{2} (x - 11) + 3

解答

极大值 (0, 3), 极小值 (\frac{22}{3}, - \frac{26539}{27})

求解步骤

f^{'} (x) = 5 x (3 x - 22)

Find intervals:

递增

: - \infty < x < 0,

递减

: 0 < x < \frac{22}{3},

递增

: \frac{22}{3} < x < \infty

将

x = 0

代入

5 x^{2} (x - 11) + 3 : 3

极大值 (0, 3)

将

x = \frac{22}{3}

代入

5 x^{2} (x - 11) + 3 : - \frac{26539}{27}

极小值 (\frac{22}{3}, - \frac{26539}{27})

极大值 (0, 3), 极小值 (\frac{22}{3}, - \frac{26539}{27})

作图

流行的例子

extreme f(x)=x^2-y^2-14x+4y+3

e x t re m e f (x) = x^{2} - y^{2} - 14 x + 4 y + 3

extreme yx^2+10x=10

e x t re m e y x^{2} + 10 x = 10

extreme y= x/2-sin(x)

e x t re m e y = \frac{x}{2} - sin (x)

extreme (x-5)/(x^2-16x+64)

e x t re m e \frac{x - 5}{x ^{2} - 16 x + 64}

extreme f(x)=(5x)/(x^2+9)

e x t re m e f (x) = \frac{5 x}{x ^{2} + 9}