extreme f(x)=(x^2-4)/(x^2+1)

解答

极值点

f (x) = \frac{x ^{2} - 4}{x ^{2} + 1}

极小值 (0, - 4)

求解步骤

f^{'} (x) = \frac{10 x}{( x ^{2} + 1 ) ^{2}}

Find intervals:

递减

: - \infty < x < 0,

递增

: 0 < x < \infty

将

x = 0

代入

\frac{x ^{2} - 4}{x ^{2} + 1} : - 4

极小值 (0, - 4)

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

e x t re m e 12 x^{5} + 120 x^{4} - 300 x^{3}

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

e x t re m e f (x, y) = 12 x y + 4321

e x t re m e f (x) = 5 x + 9