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受欢迎的函数 >

extreme f(x)=((x-4)^2)/(x+10)

解答

极值点

f (x) = \frac{( x - 4 ) ^{2}}{x + 10}

解答

极大值 (- 24, - 56), 极小值 (4, 0)

求解步骤

f^{'} (x) = \frac{x ^{2} + 20 x - 96}{( x + 10 ) ^{2}}

Find intervals:

递增

: - \infty < x < - 24,

递减

: - 24 < x < - 10,

递减

: - 10 < x < 4,

递增

: 4 < x < \infty

将

x = - 24

代入

\frac{( x - 4 ) ^{2}}{x + 10} : - 56

极大值 (- 24, - 56)

将

x = 4

代入

\frac{( x - 4 ) ^{2}}{x + 10} : 0

极小值 (4, 0)

极大值 (- 24, - 56), 极小值 (4, 0)

作图

流行的例子

extreme f(x)=4x-1

e x t re m e f (x) = 4 x - 1

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

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

extreme f(x)= x/(x^2+100)

e x t re m e f (x) = \frac{x}{x ^{2} + 100}

extreme f(x)=4x-9x^{4/9}

e x t re m e f (x) = 4 x - 9 x^{\frac{4}{9}}

extreme f(x,y)=3x^3-9x+9xy^2

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