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受欢迎的函数 >

extreme f(x)=(x^2-0.8x+0.32)/(1.6-2x)

解答

极值点

f (x) = \frac{x ^{2} - 0.8 x + 0.32}{1.6 - 2 x}

解答

极小值 (\frac{2 ( 2 - 2 )}{5}, 0.16568 \dots), 极大值 (\frac{2 ( 2 + 2 )}{5}, - 0.96568 \dots)

求解步骤

f^{'} (x) = \frac{- 2 x ^{2} + 3.2 x - 0.64}{( 1.6 - 2 x ) ^{2}}

Find intervals:

递减

: - \infty < x < \frac{2 ( 2 - 2 )}{5},

递增

: \frac{2 ( 2 - 2 )}{5} < x < 0.8,

递增

: 0.8 < x < \frac{2 ( 2 + 2 )}{5},

递减

: \frac{2 ( 2 + 2 )}{5} < x < \infty

将

x = \frac{2 ( 2 - 2 )}{5}

代入

\frac{x ^{2} - 0.8 x + 0.32}{1.6 - 2 x} : 0.16568 \dots

极小值 (\frac{2 ( 2 - 2 )}{5}, 0.16568 \dots)

将

x = \frac{2 ( 2 + 2 )}{5}

代入

\frac{x ^{2} - 0.8 x + 0.32}{1.6 - 2 x} : - 0.96568 \dots

极大值 (\frac{2 ( 2 + 2 )}{5}, - 0.96568 \dots)

极小值 (\frac{2 ( 2 - 2 )}{5}, 0.16568 \dots), 极大值 (\frac{2 ( 2 + 2 )}{5}, - 0.96568 \dots)

作图

流行的例子

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

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

extreme f(x)=|(x-2)/(x+5)|-3

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

extreme 2x^4-x^2+5

e x t re m e 2 x^{4} - x^{2} + 5

extreme f(x)=7x^9-9x^7-5(-3.4)

e x t re m e f (x) = 7 x^{9} - 9 x^{7} - 5 (- 3.4)

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

e x t re m e f (x) = - 3 + x^{2} - 3 x - 3 x^{3} + 2 x^{5} + 4 x^{4}