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受欢迎的函数 >

extreme f(x)=(12x)/(3.5x^2+2.5)

解答

极值点

f (x) = \frac{12 x}{3.5 x ^{2} + 2.5}

解答

极小值 (- \frac{7.14286 E 15}{1.0 E 16}, - 2.02837 \dots), 极大值 (\frac{7.14286 E 15}{1.0 E 16}, 2.02837 \dots)

求解步骤

f^{'} (x) = \frac{12 ( - 3.5 x ^{2} + 2.5 )}{( 3.5 x ^{2} + 2.5 ) ^{2}}

Find intervals:

递减

: - \infty < x < - 0.84515 \dots,

递增

: - 0.84515 \dots < x < 0.84515 \dots,

递减

: 0.84515 \dots < x < \infty

将

x = - \frac{7.14286 E 15}{1.0 E 16}

代入

\frac{12 x}{3.5 x ^{2} + 2.5} : - 2.02837 \dots

极小值 (- \frac{7.14286 E 15}{1.0 E 16}, - 2.02837 \dots)

将

x = \frac{7.14286 E 15}{1.0 E 16}

代入

\frac{12 x}{3.5 x ^{2} + 2.5} : 2.02837 \dots

极大值 (\frac{7.14286 E 15}{1.0 E 16}, 2.02837 \dots)

极小值 (- \frac{7.14286 E 15}{1.0 E 16}, - 2.02837 \dots), 极大值 (\frac{7.14286 E 15}{1.0 E 16}, 2.02837 \dots)

作图

流行的例子

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

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

extreme f(x)=x(152-x)

e x t re m e f (x) = x (152 - x)

extreme f(x,y)=7x^2y+9xy^2

e x t re m e f (x, y) = 7 x^{2} y + 9 x y^{2}

extreme f(x)=x^2+xy+y^2+2x-2y+6

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

extreme f(x)=165000x-100x^2

e x t re m e f (x) = 165000 x - 100 x^{2}